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Improved stability results for discrete-time switched systems: A multiple piecewise convex Lyapunov function approach

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  • Wang, Ruihua
  • Jiao, Ticao
  • Zhang, Tao
  • Fei, Shumin

Abstract

In this paper, the stability problem is investigated for a class of discrete-time switched systems with unstable subsystems under the mode-dependent average dwell time (MDADT) switching. A multiple convex Lyapunov function (MCLF) and a multiple piecewise convex Lyapunov function (MPCLF) are firstly proposed, which are formulated in a convex combination form of positive definite matrices with quasi-time-dependent coefficients. It is pointed out in the paper that the multiple Lyapunov function (MLF) and the multiple discontinuous Lyapunov function (MDLF) can be regarded as special cases of the proposed MCLF and MPCLF, respectively. Then, the exponential stability conditions are derived by the new Lyapunov functions. Both slow switching and fast switching are exerted on stable modes and unstable modes, respectively. Finally, two numerical examples are given to demonstrate that larger stability regions and tighter MDADT bounds can be obtained by using our developed techniques compared with some recent results.

Suggested Citation

  • Wang, Ruihua & Jiao, Ticao & Zhang, Tao & Fei, Shumin, 2019. "Improved stability results for discrete-time switched systems: A multiple piecewise convex Lyapunov function approach," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 54-65.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:54-65
    DOI: 10.1016/j.amc.2019.01.065
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    References listed on IDEAS

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    1. Zhikun She & Junjie Lu & Quanyi Liang & Shuzhi Sam Ge, 2017. "Dwell time based stabilisability criteria for discrete-time switched systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(14), pages 3087-3097, October.
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    Cited by:

    1. Sun, Yuchen & Ma, Shuping, 2023. "Asynchronous output regulation for a class of linear descriptor switched systems via an error-feedback controller," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    2. Nien-Tsu Hu, 2023. "Stability Analysis for Digital Redesign of Discrete-Time Switched Systems Using H ∞ Linear Matrix Inequality," Mathematics, MDPI, vol. 11(11), pages 1-22, May.
    3. Cui, Jiahao & Wang, Ruihua & Jiao, Ticao & Fei, Shumin, 2021. "A foreseeable Lyapunov function approach for H∞ asynchronous filtering of discrete-time switched systems," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    4. Zheng, Qunxian & Xu, Shengyuan & Zhang, Zhengqiang, 2020. "Nonfragile H∞ observer design for uncertain nonlinear switched systems with quantization," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    5. Wang, Huajian & Qi, Wenhai & Zhang, Lihua & Cheng, Jun & Kao, Yonggui, 2020. "Stability and stabilization for positive systems with semi-Markov switching," Applied Mathematics and Computation, Elsevier, vol. 379(C).

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