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Mode-dependent impulsive control of positive switched systems: Stability and L1-gain analysis

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  • Xi, Qiang
  • Liu, Xinzhi

Abstract

This paper studies the stability and L1-gain problems for impulsive positive switched systems (IPSS) consisting of both unstable and stable subsystems, and proposes a mode-dependent impulsive control (MDIC) method for the first time. By means of a piecewise linear co-positive Lyapunov function (PLCLF) and using average dwell time (ADT) approach, some sufficient criteria for global exponential stability (GES) and standard L1-gain are established in terms of linear programming (LP), which can be verified conveniently by Matlab. A special impulsive controller is designed to guarantee the positivity and stability of the addressed system. Several numerical examples with simulations are provided to demonstrate the effectiveness of the obtained results.

Suggested Citation

  • Xi, Qiang & Liu, Xinzhi, 2020. "Mode-dependent impulsive control of positive switched systems: Stability and L1-gain analysis," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s096007792030672x
    DOI: 10.1016/j.chaos.2020.110276
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    References listed on IDEAS

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    1. Zhang, Junfeng & Zhao, Xudong & Cai, Xiushan, 2016. "Absolute exponential L1-gain analysis and synthesis of switched nonlinear positive systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 24-36.
    2. Li, Xiaodi & Yang, Xueyan & Huang, Tingwen, 2019. "Persistence of delayed cooperative models: Impulsive control method," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 130-146.
    3. Shanshan Hong & Yu Zhang, 2019. "Stability of switched positive linear delay systems with mixed impulses," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(16), pages 3022-3037, December.
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    Cited by:

    1. Wu, Qianqian & Yang, Dan & Li, Xiaodi, 2023. "Output tracking control for state-dependent switched systems with input delay," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Kang, Yu & Zhang, Niankun & Chen, Guoyong, 2023. "Global exponential stability of impulsive switched positive nonlinear systems with mode-dependent impulses," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    3. Fang, Qi & Wang, Mingzhu & Li, Xiaodi, 2023. "Event-triggered distributed delayed impulsive control for nonlinear systems with applications to complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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