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  • 1. Almér, S.
    et al.
    Mariéthoz, S.
    Morari, M.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Application of model predictive control and analysis of switched systems to the direct voltage control of AC-DC converters2015Ingår i: 2009 European Control Conference, ECC 2009, 2015, s. 3593-3598Konferensbidrag (Refereegranskat)
    Abstract [en]

    Recent tools for control and analysis of hybrid systems are applied to an AC-DC converter. The topology poses particularly challenging problems since it is unusually complex and the circuit parameters are such that the dynamic coupling between the AC and DC sides cannot be ignored. The paper proposes a model predictive control scheme for direct voltage control which circumvents the bandwidth limitations associated with classical cascade control. The stability and harmonic properties of the resulting closed loop system are investigated using new tools for the analysis of switched systems.

  • 2.
    Almér, Stefan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Fujioka, Hisaya
    KTH. Kyoto University, Japan.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Kao, Chung Yao
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Patino, D.
    Riedinger, P.
    Geyer, T.
    Beccuti, A.
    Papafotiou, G.
    Morari, M.
    Wernrud, A.
    Rantzer, A.
    Hybrid control techniques for switched-mode DC-DC converters part I: The step-down topology2007Ingår i: 2007 American Control Conference, IEEE , 2007, s. 5450-5457Konferensbidrag (Refereegranskat)
    Abstract [en]

    Several recent techniques from hybrid and optimal control are evaluated on a power electronics benchmark problem. The benchmark involves a number of practically interesting operating scenarios for a fixed-frequency synchronous step-down dc-dc converter. The specifications are defined such that good performance only can be obtained if the switched and nonlinear nature of the problem is respected during the design phase.

  • 3.
    Almér, Stefan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Dynamic phasor analysis of pulse-modulated systems2007Ingår i: Proceedings Of The 46th IEEE Conference On Decision And Control, Vols 1-14, 2007, s. 3938-3945Konferensbidrag (Refereegranskat)
    Abstract [en]

    The paper considers stability analysis of a general class of pulse modulated systems in a phasor dynamic framework. The dynamic phasor model exploits the cyclic nature of the modulation functions by representing the system dynamics in terms of a Fourier series expansion defined over a moving time-window. The contribution of the paper is to show that a special type of periodic Lyapunov function can be used to analyze the system and that the analysis conditions become tractable for computation after truncation. The approach provides a trade-off between complexity and accuracy that includes standard state space averaged models as a special case.

  • 4. Almér, Stefan
    et al.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Dynamic Phasor Analysis Of Pulse-Modulated Systems2012Ingår i: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 50, nr 3, s. 1110-1138Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper considers stability and harmonic analysis of a general class of pulse-modulated systems. The systems are modeled using the dynamic phasor model, which explores the cyclic nature of the modulation functions by representing the system state as a Fourier series expansion defined over a moving time window. The contribution of the paper is to show that a special type of periodic Lyapunov function can be used to analyze the system and that the analysis conditions become tractable for computation after truncation. The approach provides a trade-off between complexity and accuracy that includes standard state space averaged models as a special case. The paper also shows how the dynamic phasor model can be used to derive a frequency domain input-to-state map which is analogous to the harmonic transfer function.

  • 5.
    Almér, Stefan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Harmonic analysis of pulse-width modulated systems2009Ingår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, nr 4, s. 851-862Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The paper considers the so-called dynamic phasor model as a basis for harmonic analysis of a class switching systems. The analysis covers both periodically switched systems and non-periodic systems where the switching is controlled by feedback. The dynamic phasor model is a powerful tool for exploring cyclic properties of dynamic systems. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems.

  • 6.
    Almér, Stefan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Harmonic Lyapunov functions in the analysis of periodically switched systems2006Ingår i: PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, s. 2759-2764Konferensbidrag (Refereegranskat)
    Abstract [en]

    The dynamic phasor model of a time-periodic system is used to derive a stability test involving a harmonic Lyapunov function. This reveals a new interpretation of the harmonic Lyapunov function with an appealing time-domain representation. Most importantly, it indicates that the ideas behind the harmonic Lyapunov equation can be generalized to include cyclic switching systems that have different pulse form in each period.

  • 7.
    Almér, Stefan
    et al.
    KTH, Tidigare Institutioner, Matematik.
    Jönsson, Ulf
    KTH, Tidigare Institutioner, Matematik.
    Kao, Chung-Yao
    KTH, Tidigare Institutioner, Matematik.
    Mari, Jorge
    Global stability analysis of DC-DC converters using sampled-data modeling2004Ingår i: PROCEEDINGS OF THE 2004 AMERICAN CONTROL CONFERENCE, VOLS 1-6, 2004, s. 4549-4554Konferensbidrag (Refereegranskat)
    Abstract [en]

    The paper presents stability analysis of a class of pulse-width modulated (PWM) systems which incorporates many different DC-DC converters. Two types of pulse-width modulation (digital and analog control) are considered. A procedure is developed for systematic search for Lyapunov functions. The state space is partitioned in such a way that stability is verified if a set of coupled Linear Matrix Inequalities (LMIs) is feasible. Global stability is considered as well as the computation of local regions of attraction.

  • 8.
    Almér, Stefan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Kao, Chung-Yao
    Univ Melbourne, Dept Elect & Elect Engn.
    Mari, Jorge
    GE Global Res, Elect Energy Syst.
    Stability analysis of a class of PWM systems2007Ingår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 52, nr 6, s. 1072-1078Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This note considers stability analysis of a class of pulsewidth modulated (PWM) systems that incorporates several different switched mode dc-de- converters. The systems of the class typically have periodic solutions. A sampled data model is developed and used to prove stability of these solutions. Conditions for global and local exponential stability are derived using quadratic and piecewise quadratic Lyapunov functions. The state space is partitioned and the stability conditions are verified by checking a set of coupled linear matrix inequalities (LMIs).

  • 9.
    Almér, Stefan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Dynamic phasor analysis of a class of PWM systems2015Ingår i: 2007 European Control Conference, ECC 2007, 2015, s. 1940-1947Konferensbidrag (Refereegranskat)
    Abstract [en]

    The paper makes use of the so-called dynamic phasor model for stability and performance analysis of a class of PWM systems. The dynamic phasor model allows for the state to be represented in the frequency domain where a harmonic Lyapunov function is defined. The analysis covers both periodically switched systems and non-periodic systems where the switching is controlled by feedback.

  • 10.
    Almér, Stefan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Dynamic Phasor Analysis of Periodic Systems2009Ingår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 54, nr 8, s. 2007-2012Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The paper considers stability analysis of linear time-periodic (LTP) systems based on the dynamic phasor model (DPM). The DPM exploits the periodicity of the system by expanding the system state in a Fourier series over a moving time window. This results in an L-2-equivalent representation in terms of an infinite-dimensional LTI system which describes the evolution of time varying Fourier coefficients. To prove stability, we consider quadratic time-periodic Lyapunov candidates. Using the DPM, the corresponding time-periodic Lyapunov inequality can be stated as a finite dimensional inequality and the Lyapunov function can be found by solving a linear matrix inequality.

  • 11. Beccuti, A. G.
    et al.
    Papafotiou, G.
    Morari, M.
    Almér, Stefan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Fujioka, Hisaya
    KTH. Kyoto University, Japan.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Kao, Chung Yao
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. University of Melbourne, Australia.
    Wernrud, A.
    Rantzer, A.
    Bâja, M.
    Comierais, H.
    Buisson, J.
    Hybrid control techniques for switched-mode DC-DC converters part II: The step-up topology2007Ingår i: 2007 American Control Conference, Vols 1-13, 2007, s. 5464-5471Konferensbidrag (Refereegranskat)
    Abstract [en]

    Several recent techniques from hybrid and optimal control are evaluated on a power electronics benchmark problem. The benchmark involves a number of practically interesting operating scenarios for a fixed-frequency step-up dc-dc converter. The specifications are defined such that good performance can only be obtained if the switched and nonlinear nature of the problem is respected during the design phase.

  • 12. Briat, C.
    et al.
    Yavuz, E.A
    Hjalmarsson, Håkan
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Jönsson, Ulf T.
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Karlsson, Gunnar
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    The Conservation of Information, Towards an Axiomatized Modular Modeling Approach to Congestion Control2015Ingår i: IEEE/ACM Transactions on Networking, ISSN 1063-6692, E-ISSN 1558-2566, Vol. 23, nr 3, s. 851-865Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We derive a modular fluid-flow network congestion control model based on a law of fundamental nature in networks: the conservation of information. Network elements such as queues, users, and transmission channels and network performance indicators like sending/acknowledgment rates and delays are mathematically modeled by applying this law locally. Our contributions are twofold. First, we introduce a modular metamodel that is sufficiently generic to represent any network topology. The proposed model is composed of building blocks that implement mechanisms ignored by the existing ones, which can be recovered from exact reduction or approximation of this new model. Second, we provide a novel classification of previously proposed models in the literature and show that they are often not capable of capturing the transient behavior of the network precisely. Numerical results obtained from packet-level simulations demonstrate the accuracy of the proposed model.

  • 13.
    Briat, Corentin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Karlsson, Gunnar
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsnät. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Nonlinear state-dependent delay modeling and stability analysis of internet congestion control2010Ingår i: 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2010, s. 1484-1491Konferensbidrag (Refereegranskat)
    Abstract [en]

    It is shown that the queuing delay involved in the congestion control algorithm is state-dependent and does not depend on the current time. Then, using an accurate formulation for buffers, networks with arbitrary topologies can be built. At equilibrium, our model reduces to the widely used setup by Paganini et al. Using this model, the delay-derivative is analyzed and it is proved that the delay time-derivative does not exceed one for the considered topologies. It is then shown that the considered congestion control algorithm globally stabilizes a delay-free single buffer network. Finally, using a specific linearization result for systems with state-dependent delays from Cooke and Huang, we show the local stability of the single bottleneck network.

  • 14.
    Briat, Corentin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Karlsson, Gunnar
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsnät. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Yavuz, Emre Altug
    KTH, Skolan för elektro- och systemteknik (EES), Kommunikationsnät.
    An axiomatic fluid-flow model for congestion control analysis2011Ingår i: 2011 50th IEEE Conference on Decision and Control andEuropean Control Conference (CDC-ECC), 2011, s. 3122-3129Konferensbidrag (Refereegranskat)
    Abstract [en]

    An axiomatic model for congestion control isderived. The proposed four axioms serve as a basis for theconstruction of models for the network elements. It is shownthat, under some assumptions, some models of the literature canbe recovered. A single-buffer/multiple-users topology is finallyderived and studied for illustration.

  • 15.
    Briat, Corentin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Dynamic equations on time-scale: Application to stability analysis and stabilization of aperiodic sampled-data systems2011Ingår i: IFAC Proc. Vol. (IFAC-PapersOnline), 2011, nr PART 1, s. 11374-11379Konferensbidrag (Refereegranskat)
    Abstract [en]

    The stability analysis of systems with aperiodic sampling is analyzed in the framework of dynamic equations on time-scales. Lyapunov theory is used, with sample-period-dependent and independent Lyapunov functions, to obtain stability conditions expressed in terms of parameter dependent matrix inequalities. The examples illustrate the efficiency of the approach which is able to recover, for some systems, the theoretical results for the periodic sampling case even in the aperiodic case. It is also shown that some systems may have admissible varying sampling periods located in disjoint sets. Finally, stabilization results via switching statefeedback are provided; both robust and sampling-period-dependent controllers are considered. It is shown that the latter ones, using the information on the sampling period, can improve stability properties. Stabilization examples illustrate the effectiveness of the approach.

  • 16. Cantoni, M.
    et al.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Kao, C. -Y
    IQC robustness analysis for feedback interconnections of unstable distributed parameter systems2009Ingår i: Proceedings of the 48th IEEE Conference on Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009, IEEE , 2009, s. 1124-1130Konferensbidrag (Refereegranskat)
    Abstract [en]

    In recent work the authors combined integral-quadratic-constraint (IQC) based analysis with ν-gap metric based analysis to study the robustness of feedback interconnections of possibly unstable rational transfer functions. This is extended here to the case of irrational transfer functions without pure delays. Specifically, we restrict attention to the sub-algebra of Callier-Desoer class transfer functions that have a limit at infinity.

  • 17. Cantoni, Michael
    et al.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Kao, Chung-Yao
    Robustness Analysis for Feedback Interconnections of Distributed Systems via Integral Quadratic Constraints2012Ingår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 57, nr 2, s. 302-317Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A framework is established for directly accommodating feedback interconnections of unstable distributed-parameter transfer functions in robust stability analysis via integral quadratic constraints (IQCs). This involves transfer function homotopies that are continuous in a nu-gap metric sense. As such, the development includes the extension of nu-gap metric concepts to an irrational setting and the study of uncertainty-set connectedness in these terms. The main IQC based robust stability result is established for constantly-proper transfer functions in the Callier-Desoer algebra; i.e. finitely many unstable poles and a constant limit at infinity. Problems of structured robust stability analysis and robust performance analysis are considered to illustrate use of the main result. Several numerical examples are also presented. These include stability analysis of an autonomous system with uncertain time-delay and a closed-loop control system, accounting for both the gain and phase characteristics of the distributed-parameter uncertainty associated with the nominal rational plant model used for controller synthesis.

  • 18. Cantoni, Michael
    et al.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Khong, Sei Zhen
    Robust Stability Analysis For Feedback Interconnections Of Time-Varying Linear Systems2013Ingår i: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 51, nr 1, s. 353-379Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Feedback interconnections of causal linear systems are studied in a continuous-time setting. The developments include a linear time-varying (LTV) generalization of Vinnicombe's nu-gap metric and an integral-quadratic-constraint-based robust L-2-stability theorem for uncertain feedback interconnections of potentially open-loop unstable systems. These main results are established in terms of Toeplitz-Wiener-Hopf and Hankel operators, and the Fredholm index, for a class of causal linear systems with the following attributes: (i) a system graph (i.e., subspace of L-2 input-output pairs) admits normalized strong right (i.e., image) and left (i.e., kernel) representations, and (ii) the corresponding Hankel operators are compact. These properties are first verified for stabilizable and detectable LTV state-space models to initially motivate the abstract formulation, and subsequently verified for frequency-domain multiplication by constantly proper Callier-Desoer transfer functions in analysis that confirms consistency of the developments with the time-invariant theory. To conclude, the aforementioned robust stability theorem is applied in an illustrative example concerning the feedback interconnection of distributed-parameter systems over a network with time-varying gains.

  • 19. Di Bernardo, Mario
    et al.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Jönsson, Ulf
    KTH, Tidigare Institutioner, Matematik.
    Vasca, Francesco
    On the robustness of periodic solutions in relay feedback systems2002Ingår i: Proceedings of the 15th IFAC World Congress, 2002, IFAC , 2002Konferensbidrag (Refereegranskat)
    Abstract [en]

    Structural robustness of limit cycles in relay feedback systems is studied. Motivated by a recent discovery of a novel class of bifurcations in these systems, it is illustrated through numerical simulation that small relay perturbations may change the appearance of closed orbits dramatically. It is shown analytically that certain stable periodic solutions in relay feedback systems are robust to relay perturbations.

  • 20.
    Fischione, Carlo
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Fast-Lipschitz optimization with wireless sensor networks applications2011Ingår i: Proceedings of the 10th ACM/IEEE International Conference on Information Processing in Sensor Networks, IPSN'11, 2011, s. 378-389Konferensbidrag (Refereegranskat)
    Abstract [en]

    Motivated by the need for fast computations demanded by wireless sensor networks, the new F-Lipschitz optimization theory is introduced for a novel class of optimization problems. These problems are defined by simple qualifying properties specified in terms of increasing objective function and contractive constraints. It is shown that feasible F-Lipschitz problems have always a unique optimal solution that satisfies the constraints at equality. The solution is obtained quickly by asynchronous algorithms of certified convergence. F-Lipschitz optimization can be applied to both centralized and distributed optimization. Compared to traditional Lagrangian methods, which often converge linearly, the convergence time of centralized F-Lipschitz problems is at least superlinear. Distributed F-Lipschitz algorithms converge fast, as opposed to traditional La-grangian decomposition and parallelization methods, which generally converge slowly and at the price of many message passings. In both cases, the computational complexity is much lower than traditional Lagrangian methods. Examples of application of the new optimization method are given for distributed detection and radio power control in wireless sensor networks. The drawback of the F-Lipschitz optimization is that it might be difficult to check the qualifying properties. For more general optimization problems, it is suggested that it is convenient to have conditions ensuring that the solution satisfies the constraints at equality.

  • 21. Fujioka, H.
    et al.
    Almér, Stefan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Kao, C. -Y
    Control synthesis for a class of PWM systems for robust tracking and H ∞ performance2006Ingår i: Proc IEEE Conf Decis Control, 2006, s. 4861-4866Konferensbidrag (Refereegranskat)
    Abstract [en]

    Robust control with robust tracking is considered for a class of pulse-width modulated systems (PWM) that appear, for example, in power electronics applications. The control objective is to regulate a high frequency ripple signal to robustly track a constant reference signal in an average sense. To achieve this goal, a new H∞ -control problem with integral action and averaged sampling is proposed. The design procedure is verified on a synchronous buck converter.

  • 22. Fujioka, H.
    et al.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Characterizing uncertain time-varying parameters with periodic reset2009Ingår i: 2009 American Control Conference, 2009, s. 3754-3756Konferensbidrag (Refereegranskat)
    Abstract [en]

    A number of quadratic constraints are derived for an uncertain real parameter which is slowly time-varying and periodically resetting. A finite-horizon version of the swapping lemma and a finite dimensional condition for computing the norm of related time-varying finite-horizon systems are derived.

  • 23. Fujioka, H.
    et al.
    Kao, C. -Y
    Almér, Stefan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    LQ optimal control synthesis for a class of pulse modulated systems2005Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider linear quadratic optimal control for a class of pulse-width-modulated systems. The problem is motivated from a practical application - digital control of switching power converters. The control synthesis problem is posed based on a sampled data model of the original switching dynamics and a linear quadratic criterion that takes the inter sampling behavior into account.

  • 24. Fujioka, H.
    et al.
    Kao, C. -Y
    Almér, Stefan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Sampled-data H∞ control design for a class of PWM systems2005Ingår i: Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, 2005, s. 4499-4504Konferensbidrag (Refereegranskat)
    Abstract [en]

    Robust control of a class of switched dynamical systems is considered. The switching is controlled by pulse-width modulation (PWM). This idea is used, for example, in power electronics for power conversion. The class of systems considered includes digitally controlled power converters of many different types. The traditional approach to control design for power converters rely on an averaged model that ignores the high frequency behavior and the inherent time delay due to sampling. In contrast, the method presented here is based on a sampled-data model which takes the switched nature of the system into account. The sampled-data model is approximated by a linear quadratic model to which sampled-data H∞ theory can be extended. The approach is applied to a bidirectional boost converter which is subjected to a large load disturbance.

  • 25. Fujioka, Hisaya
    et al.
    Kao, Chung-Yao
    Almér, Stefan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    LQ optimal control for a class of pulse width modulated systems2007Ingår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 43, nr 6, s. 1009-1020Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider linear quadratic optimal control for a class of pulse width modulated systems. The problem is motivated from a practical application-digital control of switching power converters. The control synthesis problem is posed based on a sampled data model of the original switching dynamics and a linear quadratic criterion that takes the intersampling behavior into account.

  • 26. Fujioka, Hisaya
    et al.
    Kao, Chung-Yao
    Almér, Stefan
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Robust tracking with H-infinity performance for PWM systems2009Ingår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, nr 8, s. 1808-1818Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Control synthesis for robust tracking is considered for a class of pulse-width modulated systems that appear, for example, in power electronics applications. The control objective is to regulate a high frequency ripple signal to robustly track a constant reference signal in an average sense. To achieve this goal, a new H-infinity control problem with integral action and average sampling is proposed. The solution of this problem involves a hybrid lifting framework which requires a careful elaboration in order to develop an algorithm that allows one to solve the design problem by the standard state space formulas for H-infinity control. The design procedure is verified on a synchronous buck converter.

  • 27.
    Heinrich, Benjamin C.
    et al.
    University of Stuttgart.
    Möller, Anders
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Local Stability of High Order Power Control in Cellular Networks2011Ingår i: 2011 50th IEEE Conference on Decision and Control and European Control Conference, 2011, s. 4528-4534Konferensbidrag (Refereegranskat)
    Abstract [en]

    We address three major control challenges present in power control of wireless cellular networks: time-delays, interference and the binary control feedback. The power control is distributed and based on measurements of the Signal-to-Interference Ratio (SIR). This implies that the users are coupled through the mutual interference.

    In this paper we show that the interference feedback plays a fundamental role for system stability and behavior. The interference is captured by the so-called feasibility matrix, which contains the interference couplings weighted with SIR-requirements. First, we consider a simplified system and derive a Nyquist stability criterion which separates the system dynamics from the eigenvalues of the feasibility matrix. This criterion is also used to derive bounds on the rate of convergence. Second, we investigate oscillations caused by the binary feedback using harmonic balance techniques. Here, we obtain a similar separation result. Using the structure of the feasibility matrix we derive bounds on the eigenvalue location, which can be seen as a robustness result to disturbances. In an example we illustrate the stability results and predict and observe oscillation modes that are caused by the interference feedback.

  • 28.
    Hu, Xiaoming
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Jönsson, UlfKTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.Wahlberg, BoKTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.Ghosh, BijoyTexas Tech University, USA.
    Three Decades of Progress in Control Sciences: Dedicated to Chris Byrnes and Anders Lindquist2010Samlingsverk (redaktörskap) (Övrigt vetenskapligt)
    Abstract [en]

    Features contributions from experts in  control research

    • Celebrates the 60th birthday of Chris Byrnes and Anders Lindquist
    • Has a celebrative flavor and at the same time contains reference material for researchers interested in control theory

    In this edited collection we commemorate the 60th birthday of Prof. Christopher Byrnes and the retirement of Prof. Anders Lindquist from the Chair of Optimization and Systems Theory at KTH. These papers were presented in part at a 2009 workshop in KTH, Stockholm, honoring the lifetime contributions of Professors Byrnes and Lindquist in various fields of applied mathematics.

  • 29. Ianelli, L.
    et al.
    Johansson, Karl Henrik
    KTH, Tidigare Institutioner, Signaler, sensorer och system.
    Jönsson, Ulf
    KTH, Tidigare Institutioner, Matematik.
    Vasca, F.
    Analysis of dither in relay feedback systems2002Ingår i: PROCEEDINGS OF THE 41ST IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, IEEE , 2002, s. 4425-4430Konferensbidrag (Refereegranskat)
    Abstract [en]

    Dither signals provide an effective way of compensating for nonlinearities in control systems. The seminal, works by Zames and Shneydor and more recently by Mossaheb present rigorous tools for systematic design of dithered systems. Their results rely however on a Lipschitz assumption on the nonlinearity and thus do not cover important applications with discontinuities. This paper presents initial results on how to analyze and design dither in nonsmooth systems. In particular, it is shown that a dithered relay feedback system can be approximated by a smoothed system obtained through an averaging approach. Guidelines are given for tuning the amplitude and the period time of the dither signal, in order to stabilize the nonsmooth system.

  • 30. Ianelli, Luigi
    et al.
    Johansson, Karl Henrik
    KTH, Tidigare Institutioner, Signaler, sensorer och system.
    Jönsson, Ulf
    KTH, Tidigare Institutioner, Matematik.
    Vasca, F.
    Practical stability and limit cycles of dithered relay feedback systems2003Konferensbidrag (Refereegranskat)
    Abstract [en]

    A new constructive way for choosing dither amplitude and frequency in order to effectively stabilize relay feedback systems by triangular dither is proposed. It is argued that the proposed averaging approach is not easily extended to square dither signals. Trajectories composed by smooth and switching parts are also analyzed and their relationship with limit cycles exhibited by the smoothed system is investigated.

  • 31. Ianelli, Luigi
    et al.
    Johansson, Karl Henrik
    KTH, Tidigare Institutioner, Signaler, sensorer och system.
    Jönsson, Ulf
    KTH, Tidigare Institutioner, Matematik.
    Vasca, Francesco
    Dither shape in the averaging of switched systems2004Ingår i: PROCEEDINGS OF THE 2004 AMERICAN CONTROL CONFERENCE, VOLS 1-6, IEEE , 2004, s. 5812-5817Konferensbidrag (Refereegranskat)
    Abstract [en]

    It was shown by Zames and Shneydor that a high-frequency dither of a quite arbitrary shape can be used to smooth the effective nonlinear sector of Lipschitz continuous feedback systems. Here it is shown that also systems with discontinuous nonlinearities can be smoothed using dither signals, as long as the amplitude distribution function of the dither is Lipschitz continuous.

  • 32. Ianelli, Luigi
    et al.
    Johansson, Karl Henrik
    KTH, Tidigare Institutioner, Signaler, sensorer och system.
    Jönsson, Ulf
    KTH, Tidigare Institutioner, Matematik.
    Vasca, Francesco
    Effects of dither shapes in nonsmooth feedback systems: experimental results and theoretical insight2003Ingår i: Proceedings of the 42nd IEEE Conference on Decision and Control, Vols. 1-6, IEEE , 2003, s. 4285-4290Konferensbidrag (Refereegranskat)
    Abstract [en]

     Dither signals are commonly used to compensate for nonlinearities in feedback systems in electronics and mechanics. Recently, theoretical results were proposed for the analysis or a particularly interesting class of nonsmooth systems, namely relay feedback systems with triangular dither. In this paper the class of dither signals is enlarged by considering square and trapezoidal dither: it is shown how the dither shape affects the behavior of nonsmooth feedback systems, differently from the case of dither in Lipschitz continuous systems. Experimental results support this fact and a theoretical insight is given in order to explain the phenomena.

  • 33. Iannelli, L.
    et al.
    Johansson, K. H.
    Jönsson, Ulf T.
    KTH, Tidigare Institutioner                               , Matematik.
    Vasca, F.
    Analysis of periodically forced uncertain feedback systems2003Ingår i: IEEE Transactions on Circuits And Systems Part I: Fundamental Theory and Applications, ISSN 1057-7122, E-ISSN 1558-1268, Vol. 50, nr 2, s. 244-258Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Conditions for existence and stability of stationary periodic solutions of uncertain periodic systems are addressed in this paper. Existence and harmonic performance are studied using integral quadratic constraints (IQCs) defined on the space of square integrable periodic functions. Stability is investigated using IQCs defined on the usual space of square integrable functions. The analysis results in criteria formulated as affinely parameterized operator inequalities. Methods of convex optimization are used to find feasible parameters. Two applications will be discussed. The first is harmonic analysis of an electronic circuit and the second involves estimation of the amplitude of a periodic disturbance in a nonlinear control system.

  • 34. Iannelli, Luigi
    et al.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Vasca, F.
    Subtleties in the averaging of hybrid systems with applications to power electronics2006Ingår i: Analysis and Design of Hybrid Systems 2006, Elsevier, 2006, s. 247-252Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    Abstract [en]

    Dither signals are commonly used in electronics for implementing different type of modulations in power converters, which represent a very interesting class of hybrid systems. It was recently shown that a non-smooth dithered system can be approximated by an averaged system if the dither frequency is sufficiently high and that the amplitude distribution function of the dither is continuous and has bounded derivative. In power electronics, a large class of systems can be modeled as hybrid dynamical systems due to the presence of switching devices (for instance diodes or transistors) that "instantaneously" change the dynamical behavior of the system. This class of systems can be adequately represented by hybrid systems or nonlinear differential equations with discontinuous nonlinearities. One of the standard approaches for designing control algorithms for power converters is to use modulation schemes (e.g. pulse width modulation, PWM).

  • 35. Iannelli, Luigi
    et al.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Vasca, Francesco
    Subtleties in the averaging of a class of hybrid systems with applications to power converters2008Ingår i: Control Engineering Practice, ISSN 0967-0661, E-ISSN 1873-6939, Vol. 16, nr 8, s. 961-975Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    High-frequency dither signals are commonly used to implement modulation schemes in power electronics converters. These systems represent an interesting class of hybrid systems with external excitation. They have a rich dynamical behavior, which cannot be easily understood intuitively. Despite the common use of averaging techniques in power electronics, it was only recently proved that a dithered hybrid system can be approximated by an averaged system under certain conditions on the dither signal. Averaging and averaged models for various types of power converters are analyzed in the paper. It is shown that the averaged nonlinearity depends on the dither shape and that dither signals with Lipschitz-continuous averaged nonlinearities can be used to adapt the equivalent gain of power converters. Practical stability of the original dithered system can be inferred by analyzing a simpler averaged system. The main contribution of the paper is to show that the averaged and the dithered systems may have drastically different behavior if the assumptions of the recently developed averaging theory for dithered hybrid systems are violated. Several practical experiments and simulation examples of power electronics converters are discussed. They indicate that the conditions on the dither signal imposed by the averaging theory are rather tight.

  • 36. Iannelli, Luigi
    et al.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Vasca, Francesco
    Subtleties in the averaging of hybrid systems with application to power electronics2006Ingår i: 2nd IFAC Conference on Analysis and Design of Hybrid Systems, 2006 / [ed] C.G. Cassandras, A. Giua, C. Seatzu, J. Zaytoon, IFAC , 2006Konferensbidrag (Refereegranskat)
    Abstract [en]

    Dither signals are commonly used in electronics for implementing different type of modulations in power converters, which represent a very interesting class of hybrid systems. It was recently shown that a nonsmooth dithered system can be approximated by an averaged system provided that the dither frequency is sufficiently high and that the amplitude distribution function of the dither is absolutely continuous and has bounded derivative. This result is exploited in this paper for power converters. Averaged models corresponding to various shapes of dither signal are analyzed, showing that dither with Lipschitz continuous amplitude distribution function can be used to adapt the equivalent gain of the power converter.

  • 37.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    A sector condition for local robustness of limit cycles2006Ingår i: 2006 American Control Conference, Vols 1-12, 2006, Vol. 1-12, s. 5014-5019Konferensbidrag (Refereegranskat)
    Abstract [en]

    Robustness of periodic oscillations in autonomous feedback systems are considered for systems with separable nonlinearities. Local quadratic separation of the nonlinear dynamics from the linear part of the dynamics is used to characterize a set of systems that exhibit periodic oscillation in a bounded frequency and amplitude range. The main analysis condition can be formulated as a feasibility problem for linear matrix inequalities.

  • 38.
    Jönsson, Ulf
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Analysis and design of oscillator networks2006Ingår i: 2006 Chinese Control Conference, Vols 1-5, 2006, s. 1319-1324Konferensbidrag (Refereegranskat)
    Abstract [en]

    The design and analysis of oscillator networks raises a number fundamental questions in systems and control. The existence, uniqueness, and location of periodic solutions of dynamical systems as well as the stability and robusmess of these solutions are all challenging problems that must be addressed in design and analysis of such networks. In this paper we investigate local stability and robustness properties of oscillator networks. The focus is on how the design of the network interconnection matrix affects both convergence and robustness of the network.

  • 39.
    Jönsson, Ulf
    KTH, Tidigare Institutioner, Matematik.
    Local robustness of oscillator networks2004Ingår i: 2004 43RD IEEE CONFERENCE ON DECISION AND CONTROL (CDC), VOLS 1-5, 2004, s. 4649-4654Konferensbidrag (Refereegranskat)
    Abstract [en]

    Conditions for robust stability of networks of identical coupled oscillators are derived. Local stability as well as the computation of a robustness margin is considered.

  • 40.
    Jönsson, Ulf
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Cantoni, M.
    Kao, C. -Y
    On Structured Robustness Analysis for Feedback Interconnections of Unstable Systems2008Ingår i: 47TH IEEE CONFERENCE ON DECISION AND CONTROL, 2008 (CDC 2008), 2008, s. 351-356Konferensbidrag (Refereegranskat)
    Abstract [en]

    The purpose of this paper is to broaden the scope of integral-quadratic-constraint based structured robustness analysis in a way that accommodates feedback interconnections of unstable linear time-invariant systems. This is achieved by exploring the use of Vinnicombe's nu-gap metric as a measure of distance. Various standard robustness analysis problems are revisited within the context of the main result.

  • 41.
    Jönsson, Ulf
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Kao, ChungYao
    Consensus of Heterogeneous Linear Agents Applied to a Formation Control Problem2010Ingår i: Proceedings of the IEEE Conference on Decision and Control, NEW YORK: IEEE , 2010, s. 6902-6907Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    Robustness to dynamic uncertainty is considered for consensus algorithms. The purpose of such algorithms is to use distributed control to reach an agreement regarding a certain quantity of interest that depends on the state of all systems. In distinction to the standard consensus problem where the dynamics of all individual agents are the same and of low dimension, the convergence criterion now depends on the full spectrum of the communication graph and not only the largest nonzero eigenvalue. The new consensus criterion is posed as an inverse Nyquist criterion that provides a clear separation between the individual dynamics and the spectrum of the graph. A formation control problem for a target encircling task is considered as an application.

  • 42.
    Jönsson, Ulf
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Megretski, A.
    Limit cycle analysis using a system right inverse2005Ingår i: 2005 44th IEEE Conference on Decision and Control & European Control Conference, Vols 1-8, 2005, s. 2951-2956Konferensbidrag (Refereegranskat)
    Abstract [en]

    The variational system obtained by linearizing a dynamical system along a limit cycle is always non-invertible. This follows because the limit cycle is only unique modulo time translation. It is shown that questions such as uniqueness, robustness, and computation of limit cycles can be addressed using a right inverse of the variational system. Small gain arguments are used in the analysis.

  • 43.
    Jönsson, Ulf T.
    KTH, Tidigare Institutioner                               , Matematik.
    A cutting plane algorithm for robustness analysis of periodically time-varying systems2001Ingår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 46, nr 4, s. 579-592Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    An algorithm for robustness analysis of periodic systems is derived. The system under consideration consists of a linear periodically time-varying plant in feedback interconnection with a structured uncertainty, Conditions for robust stability and robust performance can be formulated in terms of periodic integral quadratic constraints (IQCs), in this way, the robustness analysis becomes a problem of optimizing the parameters of the IQC. A cutting plane algorithm is suggested for solving this infinite-dimensional optimization problem.

  • 44.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    A SECTOR CONDITION FOR LIMIT CYCLE ROBUSTNESS2008Ingår i: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 47, nr 6, s. 2745-2772Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Robustness of periodic oscillations in autonomous feedback systems is considered for systems with separable nonlinearities. Local quadratic separation of the nonlinear dynamics from the linear part of the dynamics is used to characterize a set of systems that exhibit periodic oscillation in a bounded frequency and amplitude range. The quadratic constraint is generated as a time-periodic sector condition that characterizes the nonlinearity around a nominal periodic solution. The main analysis condition is formulated as an operator inequality involving the nominal dynamics and the sector constraint. This is an infinite dimensional robustness test that must be truncated to be verified numerically. We discuss two possible ways of performing the analysis.

  • 45.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    A small-gain theory for limit cycles of systems on lure form2005Ingår i: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 44, nr 3, s. 909-938Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Local exponential stability and local robustness for limit cycle solutions of ordinary differential equations can be verified using the characteristic multipliers. These well-known results are here generalized to a class of infinite-dimensional systems. Stability and robustness are now verified using certain invertibility conditions on the linear equations that are obtained when the system is linearized along the limit cycle. The new criterion reduces to the classical condition on the characteristic multipliers when we consider a finite-dimensional system which is perturbed by a bounded but possibly infinite-dimensional operator. The computation of a robustness margin, i.e., a bound on the maximally allowed perturbation, is also considered.

  • 46.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    A time-periodic sector condition for limit cycle robustness2007Ingår i: Proceedings Of The 46th IEEE Conference On Decision And Control, Vols 1-14, 2007, s. 1513-1519Konferensbidrag (Refereegranskat)
    Abstract [en]

    Existence and robustness of periodic oscillations in autonomous feedback systems are considered for systems with separable nonlinearities. Local quadratic separation of the nonlinear dynamics from the linear part of the dynamics is used to characterize a set of systems that exhibit periodic oscillation in a bounded frequency and amplitude band range. The quadratic constraint is generated as a time-periodic sector condition that characterizes the nonlinearity along a nominal periodic solution. The main analysis condition is formulated as an operator inequality involving the nominal dynamics and the sector constraint. This is an infinite dimensional robustness test that must be truncated to be verified numerically. We discuss two possible ways of performing the analysis.

  • 47.
    Jönsson, Ulf T.
    KTH, Tidigare Institutioner                               , Matematik.
    New results for analysis of systems with repeated nonlinearities2001Ingår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 37, nr 5, s. 739-747Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This work presents new results for analysis of systems with repeated monotonic or slope restricted nonlinearities. We first give new integral quadratic constraints (IQCs) that are satisfied by the inputs and outputs of diagonal operators with equal, monotonic or slope restricted, diagonal entries. Then, we present new analysis results For systems with repeated nonlinearities, obtained using the new IQCs. For the type of nonlinearities considered in this work, the new results are less conservative than previously known results. The computation of the new conditions is discussed. The results in this paper apply also to problems with nonrepeated nonlinearities whenever these are representable as the interconnection of multiple repeated nonlinearities and a constant matrix.

  • 48.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Primal and Dual Criteria for Robust Stability and Their Application to Systems Interconnected Over a Bipartite Graph2010Ingår i: 2010 AMERICAN CONTROL CONFERENCE , 2010, s. 5458-5464Konferensbidrag (Refereegranskat)
    Abstract [en]

    A dual formulation of a standard stability criterion from robust control is derived and investigated. The dual provides additional insight into the stability criterion and is sometimes easier to use than the primal. This is illustrated for a class of systems interconnected over a bipartite graph. The dual criterion reveals structural properties of the interconnection which in some cases are easy to investigate using low complexity tests.

  • 49.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Primal and dual criteria for robust stability applied to large scale systems2012Ingår i: Distributed Decision Making and Control, Springer, 2012, Vol. 417, s. 3-25Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    Primal and dual formulations of stability criteria based on multipliers will be discussed. The foundation for multiplier-based stability analysis is the use of a convex cone of multipliers to characterize the uncertainty in a system. The primal and dual stability criteria are formulated as convex feasibility tests involving the nominal dynamics and multipliers from the cone and the polar cone, respectively. The motivation for introducing the dual is that it provides additional insight into the stability criterion and that it is sometimes easier to use than the primal. The case considered in this chapter is that of uncertainty as it represents the interconnection of a complex network. The multipliers are used to describe characteristic properties of the network such as the spectral location or the structure of the underlying graph.

  • 50.
    Jönsson, Ulf T.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Primal and Dual Stability Criteria for Systems with Time-Varying Gains2011Ingår i: 2011 AMERICAN CONTROL CONFERENCE, 2011, s. 4354-4360Konferensbidrag (Refereegranskat)
    Abstract [en]

    Primal and dual stability criteria are derived for systems with uncertain or time-varying components that can be characterized using mixed multipliers. The constant part of the multiplier is used to model time-varying components while the frequency varying multiplier is used to model linear time-invariant uncertainties. It is shown that the dual criterion sometimes reduces to easy-to-use criteria that reveal the structure of the problem.

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