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Stability analysis of discrete-time switched linear systems with unstable subsystems

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  • Yu, Qiang
  • Zhao, Xudong

Abstract

The problem of stability for discrete-time switched linear systems (DSLSs) with unstable subsystems is investigated. Unlike most existing results that require each switching mode of the system to be asymptotically stable, this paper considers the case that each subsystem may be unstable. First, under certain hypotheses, a necessary condition of stability for DSLSs is obtained. Second, using the average dwell time (ADT) strategy, some sufficient conditions of exponential stability for switched linear systems are derived under two assumptions. Finally, two examples are presented to show the effectiveness of the proposed approaches.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:718-725
    DOI: 10.1016/j.amc.2015.10.039
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    References listed on IDEAS

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    1. 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.
    2. Xudong Zhao & Hao Liu & Zhenhuan Wang, 2013. "Weighted performance analysis of switched linear systems with mode-dependent average dwell time," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(11), pages 2130-2139.
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    Cited by:

    1. Zhou, Lei & Ding, Hui & Xiao, Xiaoqing, 2021. "Input-to-state stability of discrete-time switched nonlinear systems with generalized switching signals," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    2. Xiao, Xiaoqing & Park, Ju H. & Zhou, Lei, 2018. "Event-triggered control of discrete-time switched linear systems with packet losses," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 344-352.
    3. Mourad Kchaou & Saleh Al Ahmadi, 2017. "Robust Control for Nonlinear Uncertain Switched Descriptor Systems with Time Delay and Nonlinear Input: A Sliding Mode Approach," Complexity, Hindawi, vol. 2017, pages 1-14, June.
    4. Gao, Lijun & Liu, Zihan & Yang, Suo, 2024. "Input-to-state stability in probability of constrained impulsive switched delayed systems with unstable subsystems," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    5. Yu, Qiang & Lv, Hao, 2020. "The new stability criteria of discrete-time switched systems with an improved mode dependent average dwell time approach," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    6. Wang, Yijing & Zou, Yanchao & Zuo, Zhiqiang & Li, Hongchao, 2016. "Finite-time stabilization of switched nonlinear systems with partial unstable modes," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 172-181.

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