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  • 1.
    Briat, Corentin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Convergence and Equivalence Results for the Jensen's Inequality-Application to Time-Delay and Sampled-Data Systems2011In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 56, no 7, p. 1660-1665Article in journal (Refereed)
    Abstract [en]

    The Jensen's inequality plays a crucial role in the analysis of time-delay and sampled-data systems. Its conservatism is studied through the use of the Gruss Inequality. It has been reported in the literature that fragmentation (or partitioning) schemes allow to empirically improve the results. We prove here that the Jensen's gap can be made arbitrarily small provided that the order of uniform fragmentation is chosen sufficiently large. Nonuniform fragmentation schemes are also shown to speed up the convergence in certain cases. Finally, a family of bounds is characterized and a comparison with other bounds of the literature is provided. It is shown that the other bounds are equivalent to Jensen's and that they exhibit interesting well-posedness and linearity properties which can be exploited to obtain better numerical results.

  • 2.
    Briat, Corentin
    KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Robust stability analysis in the *-norm and Lyapunov-Razumikhin functions for the stability analysis of time-delay systems2011Conference paper (Other academic)
    Abstract [en]

    Lyapunov-Krasovskii functionals have been shown to have connections with input-output techniques considering delay operators mapping L-2 to L-2. It is shown here that Lyapunov-Razumikhin functions can also be connected to the input-output framework by considering operators on L-infinity and the corresponding Small-Gain Theorem. Several important results from the Lyapunov-Razumikhin Theorem are retrieved and extended.

  • 3.
    Briat, Corentin
    KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Robust stability analysis of uncertain Linear Positive Systems via Integral Linear Constraints: L-1- and L-infinity-gain characterizations2011Conference paper (Refereed)
    Abstract [en]

    Copositive Lyapunov functions are used along with dissipativity theory for stability analysis of uncertain linear positive systems. At the difference of standard results, linear supply-rates are employed for robustness and performance analysis and lead to L-1- and L-infinity-gain characterizations. This naturally guides to the definition of Integral Linear Constraints (ILCs) for the characterization of input-output nonnegative uncertainties. It turns out that these integral linear constraints can be linked to the Laplace domain, in order to be tuned adequately, by exploiting the L-1-norm and input/output signals properties. This dual viewpoint allows to prove that the static-gain of the uncertainties, only, is critical for stability. This fact provides a new explanation for the surprising stability properties of linear positive time-delay systems. The obtained stability and performance analysis conditions are expressed in terms of (robust) linear programming problems that are transformed into finite dimensional ones using the Handelman's Theorem. Several examples are provided for illustration.

  • 4.
    Briat, Corentin
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L-1-gain and L-infinity-gain characterization2013In: International Journal of Robust and Nonlinear Control, ISSN 1049-8923, E-ISSN 1099-1239, Vol. 23, no 17, p. 1932-1954Article in journal (Refereed)
    Abstract [en]

    Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply rates are employed here for robustness and performance analysis using L-1-gain and L-gain. Robust stability analysis is performed using integral linear constraints for which several classes of uncertainties are discussed. The approach is then extended to robust stabilization and performance optimization. The obtained results are expressed in terms of robust linear programming problems that are equivalently turned into finite dimensional ones using Handelman's theorem. Several examples are provided for illustration.

  • 5.
    Briat, Corentin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Karlsson, Gunnar
    KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Nonlinear state-dependent delay modeling and stability analysis of internet congestion control2010In: 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2010, p. 1484-1491Conference paper (Refereed)
    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.

  • 6.
    Briat, Corentin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Karlsson, Gunnar
    KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Yavuz, Emre Altug
    KTH, School of Electrical Engineering (EES), Communication Networks.
    An axiomatic fluid-flow model for congestion control analysis2011In: 2011 50th IEEE Conference on Decision and Control andEuropean Control Conference (CDC-ECC), 2011, p. 3122-3129Conference paper (Refereed)
    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.

  • 7.
    Briat, Corentin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Dynamic equations on time-scale: Application to stability analysis and stabilization of aperiodic sampled-data systems2011In: IFAC Proc. Vol. (IFAC-PapersOnline), 2011, no PART 1, p. 11374-11379Conference paper (Refereed)
    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.

  • 8.
    Briat, Corentin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Martinez, J. J.
    H ∞ bounded resilient state-feedback design for linear continuous-time systems -a robust control approach2011In: IFAC Proceedings Volumes: (IFAC-PapersOnline), 2011, no PART 1, p. 9307-9312Conference paper (Refereed)
    Abstract [en]

    The quadratic stabilization of LTI systems by bounded resilient state-feedback controllers is addressed. The controllers are guaranteed to be non-fragile with respect to either uniform or nonuniform maximal implementation errors. The design of resilient controller relies on an LMI problem while boundedness of the coefficients (a NP-Hard problem) can be guaranteed by solving a nonconvex problem involving a BMI. The latter problem is solved using proposed locally convergent iterative LMI algorithms. Finally, an example is considered in order to illustrate the effectiveness of the approach.

  • 9.
    Briat, Corentin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sename, O.
    Lafay, J. -F
    Design of LPV observers for LPV time-delay systems: an algebraic approach2011In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 84, no 9, p. 1533-1542Article in journal (Refereed)
    Abstract [en]

    The design of reduced order observer for linear parameter varying (LPV) time-delay systems is addressed. Necessary conditions guaranteeing critical structural properties for the observation error dynamics are first provided through nonlinear algebraic matrix equalities. An explicit parametrisation of the family of observers fulfilling these necessary conditions is then derived. Finally, an approach based on linear matrix inequalities is provided and used to select a suitable observer within this family, according to some criterion; e.g. maximisation of the delay margin or guaranteed suboptimal L(2)-gain. Examples from the literature illustrate the efficiency of the approach.

  • 10.
    Briat, Corentin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Sename, O.
    GIPSA-Lab, Department of Control Systems (Former LAG), Grenoble Universités.
    Lafay, J. F.
    IRCCyN - Centrale de Nantes.
    Memory-resilient gain-scheduled state-feedback control of uncertain LTI/LPV systems with time-varying delays2010In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 59, no 8, p. 451-459Article in journal (Refereed)
    Abstract [en]

    The stabilization of uncertain LTI/LPV time-delay systems with time-varying delays by state-feedback controllers is addressed. Compared to other works in the literature, the proposed approach allows for the synthesis of resilient controllers with respect to uncertainties on the implemented delay. It is emphasized that such controllers unify memoryless and exact-memory controllers usually considered in the literature. The solutions to the stability and stabilization problems are expressed in terms of LMIs which allow us to check the stability of the closed-loop system for a given bound on the knowledge error and even optimize the uncertainty radius under some performance constraints; in this paper, the H-infinity performance measure is considered. The interest of the approach is finally illustrated through several examples.

  • 11.
    Briat, Corentin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Seuret, A.
    Stability criteria for asynchronous sampled-data systems - A fragmentation approach2011In: IFAC Proc. Vol. (IFAC-PapersOnline), 2011, no PART 1, p. 1313-1318Conference paper (Refereed)
    Abstract [en]

    The stability analysis of asynchronous sampled-data systems is studied. The approach is based on a recent result which allows to study, in an equivalent way, the quadratic stability of asynchronous sampled-data systems in a continuous-time framework via the use of peculiar functionals satisfying a necessary boundary condition. The method developed here is an extension of previous results using a fragmentation technique inspired from recent advances in time-delay systems theory. The approach leads to a tractable convex feasibility problem involving a small number of finite dimensional LMIs. The approach is then finally illustrated through several examples.

  • 12.
    Briat, Corentin
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Seuret, Alexandre
    Convex Dwell-Time Characterizations for Uncertain Linear Impulsive Systems2012In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 57, no 12, p. 3241-3246Article in journal (Refereed)
    Abstract [en]

    New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of functionals suitable for the analysis of hybrid systems. This approach allows to consider Lyapunov functions that evolve nonmonotonically along the flow of the system in a new way, broadening then the admissible class of systems which may be analyzed. As a byproduct, the particular structure of the obtained conditions makes the method is easily extendable to uncertain systems by exploiting some convexity properties. Several examples illustrate the approach.

  • 13.
    Briat, Corentin
    et al.
    KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Yavuz, Emre A.
    KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Karlsson, Gunnar
    KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A conservation-law-based modular fluid-flow model for network congestion modeling2012In: 2012 Proceedings - IEEE INFOCOM, IEEE Computer Society, 2012, p. 2050-2058Conference paper (Refereed)
    Abstract [en]

    A modular fluid-flow model for network congestion analysis and control is proposed. The model is derived from an information conservation law stating that the information is either in transit, lost or received. Mathematical models of network elements such as queues, users, and transmission channels, and network description variables, including sending/ acknowledgement rates and delays, are inferred from this law and obtained by applying this principle locally. The modularity of the devised model makes it sufficiently generic to describe any network topology, and appealing for building simulators. Previous models in the literature are often not capable of capturing the transient behavior of the network precisely, making the resulting analysis inaccurate in practice. Those models can be recovered from exact reduction or approximation of this new model. An important aspect of this particular modeling approach is the introduction of new tight building blocks that implement mechanisms ignored by the existing ones, notably at the queue and user levels. Comparisons with packet-level simulations corroborate the proposed model.

  • 14.
    Briat, Corentin
    et al.
    KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Yavuz, Emre A.
    KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Karlsson, Gunnar
    KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Impact of Queueing Delay Estimation Error on Equilibrium and Its Stability2011In: NETWORKING 2011, PT II, 2011, p. 356-367Conference paper (Refereed)
    Abstract [en]

    Delay-based transmission control protocols need to separate round-trip time (RTT) measurements into their constituting parts: the propagation and the queueing delays. We consider two means for this; the first is to take the propagation delay as the minimum observed RTT value, and the second is to measure the queueing delay at the routers and feed it back to the sources. We choose FAST-TCP as a representative delay-based transmission control protocol for analysis and study the impact of delay knowledge errors on its performance. We have shown that while the first method destroys fairness and the uniqueness of the equilibrium, the stability of the protocol can easily be obtained through tuning the protocol terms appropriately. Even though the second technique is shown to preserve fairness and uniqueness of the equilibrium point, we have presented that unavoidable oscillations can occur around the equilibrium point.

  • 15.
    Demirel, Burak
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Briat, Corentin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Johansson, Mikael
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Supervisory control design for networked systems with time-varying communication delays2012In: Analysis and Design of Hybrid Systems, IFAC , 2012, p. 133-140Conference paper (Refereed)
    Abstract [en]

    This paper proposes a supervisory control structure for networked systems with time-varying delays. The control structure, in which a supervisor triggers the most appropriate controller from a multi-controller unit, aims at improving the closed-loop performance relative to what can be obtained using a single robust controller. Our analysis considers average dwelltime switching and is based on a novel multiple Lyapunov-Krasovskii functional. We develop analysis conditions that can be verified by semi-definite programming, and show that associated state feedback synthesis problem also can be solved using convex optimization. Small and large scale networked control systems are used to illustrate the effectiveness of our approach.

  • 16.
    Olofsson, K Erik J
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Witrant, Emmanuel
    UJF/INPG.
    Briat, Corentin
    UJF/INPG.
    Niculescu, Silviu-Iulian
    CNRS/Supelec Laboratoire des Signaux et Systemes, Gif-sur-Yvette, France.
    Brunsell, Per
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Stability analysis and model-based control in EXTRAP-T2R with time-delay compensation2008In: Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, Dec. 9-11, 2008, IEEE conference proceedings, 2008, p. 2044-2049Conference paper (Refereed)
    Abstract [en]

    In this paper, we investigate the stability problems and control issues that occur in a reversed-field pinch (RFP) device, EXTRAP-T2R (T2R), used for research in fusion plasma physics and general plasma (ionized gas) dynamics. The plant exhibits, among other things, magnetohydrodynamic instabilities known as resistive-wall modes (RWMs), growing on a time-scale set by a surrounding non-perfectly conducting shell.We propose a novel model that takes into account experimental constraints, such as the actuators dynamics and control latencies, which lead to a multivariable time-delay model of the system. The open-loop field-error characteristics are estimated and a stability analysis of the resulting closed-loop delay differential equation (DDE) emphasizes the importance of the delay effects. We then design a structurally constrained optimal PID controller by direct eigenvalue optimization (DEO) of this DDE. The presented results are substantially based on and compared with experimental data.

  • 17. Witrant, Emmanuel
    et al.
    Di Marco, Piergiuseppe
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Park, Pan Gun
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Briat, Corentin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Limitations and performances of robust control over WSN: UFAD control in intelligent buildings2010In: IMA Journal of Mathematical Control and Information, ISSN 0265-0754, E-ISSN 1471-6887, Vol. 27, no 4, p. 527-543Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to propose a model-based feedback control strategy for indoor temperature regulation in buildings equipped with underfloor air distribution. Supposing distributed sensing and actuation capabilities, a zero-dimensional model of the ventilation process is derived, based on the thermodynamics properties of the flow. A state-space description of the process is then inferred, including discrete events and non-linear components. The use of a wireless sensor network and the resulting communication constraints with the IEEE 802.15.4 standard are discussed. Both synchronous and asynchronous transmissions are considered. Based on the linear part of the model, different H-infinity robust multiple-input multiple-output (MIMO) controllers are designed, first with a standard mixed-sensitivity approach and then by taking into account the network-induced delay explicitly. The impact of the communication constraints and the relative performances of the controllers are discussed based on simulation results.

1 - 17 of 17
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