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Stability of Positive Switched Linear Systems: Weak Excitation and Robustness to Time-Varying Delay
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0001-9940-5929
2017 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 1, 399-405 p., 7409998Article in journal (Refereed) Published
Abstract [en]

This article investigates the stability of positive switched linear systems. We start from motivating examples and focus on the case when each switched subsystem is marginally stable (in the sense that all the eigenvalues of the subsystem matrix are in the closed left-half plane with those on the imaginary axis simple) instead of asymptotically stable. A weak excitation condition is first proposed such that the considered positive switched linear system is exponentially stable. An extension to the case without dwell time assumption is also presented. Then, we study the influence of time-varying delay on the stability of the considered positive switched linear system. We show that the proposed weak excitation condition for the delay-free case is also sufficient for the asymptotic stability of the positive switched linear system under unbounded time-varying delay. In addition, it is shown that the convergence rate is exponential if there exists an upper bound for the delay, irrespective of the magnitude of this bound. The motivating examples are revisited to illustrate the theoretical results.

Place, publisher, year, edition, pages
IEEE, 2017. Vol. 62, no 1, 399-405 p., 7409998
Keyword [en]
Eigenvalues, positive switched linear systems, time-varying delay, Asymptotic stability, Eigenvalues and eigenfunctions, Linear systems, Motivation, Stability, Switching systems, Time delay, Time varying control systems, Asymptotically stable, Convergence rates, Excitation conditions, Exponentially stable, Imaginary axis, Switched linear system, Time varying- delays, System stability
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-202837DOI: 10.1109/TAC.2016.2531044ScopusID: 2-s2.0-85009911220OAI: oai:DiVA.org:kth-202837DiVA: diva2:1082962
Note

QC 20170320

Available from: 2017-03-20 Created: 2017-03-20 Last updated: 2017-03-20Bibliographically approved

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  • apa
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