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Robust stability analysis of uncertain switched linear systems with unstable subsystems

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  • Qiang Yu
  • Baowei Wu

Abstract

The problem of robust stability for switched linear systems with all the subsystems being unstable is investigated. Unlike the most existing results in which each switching mode in the system is asymptotically stable, the subsystems may be unstable in this paper. A necessary condition of stability for switched linear systems is first obtained with certain hypothesis. Then, under two assumptions, sufficient conditions of exponential stability for both deterministic and uncertain switched linear systems are presented by using the invariant subspace theory and average dwell time method. Moreover, we further develop multiple Lyapunov functions and propose a method for constructing multiple Lyapunov functions for the considered switched linear systems with certain switching law. Several examples are included to show the effectiveness of the theoretical findings.

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  • Qiang Yu & Baowei Wu, 2015. "Robust stability analysis of uncertain switched linear systems with unstable subsystems," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(7), pages 1278-1287, May.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:7:p:1278-1287
    DOI: 10.1080/00207721.2013.816089
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    References listed on IDEAS

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    1. Tai-Fang Li & Georgi Dimirovski & Yanyan Liu & Jun Zhao, 2013. "Improved stability of a class of switched neutral systems via Lyapunov–Krasovskii functionals and an average dwell-time scheme," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(6), pages 1076-1088.
    2. Ben Niu & Jun Zhao, 2013. "Tracking control for output-constrained nonlinear switched systems with a barrier Lyapunov function," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(5), pages 978-985.
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    Cited by:

    1. Zhou, Yusheng & Chen, Danhong, 2021. "Optimized state-dependent switching law design for a class of switched nonlinear systems with two unstable subsystems," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    2. Yu, Qiang & Zhao, Xudong, 2016. "Stability analysis of discrete-time switched linear systems with unstable subsystems," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 718-725.

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