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On stabilizability of switched positive linear systems under state-dependent switching

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  • Ding, Xiuyong
  • Liu, Xiu

Abstract

This paper addresses the stabilization of switched positive linear systems by state-dependent switching. We show that if there is a Hurwitz convex (or linear) combination of the coefficient matrices, then the switched positive linear system can be exponentially stabilized by means of a single linear co-positive Lyapunov function. If there is not a stable combination of system matrices, it is shown that the exponential stabilizability is equivalent to a completeness condition on the coefficient matrices. When the switched positive systems can not be stabilized by the single Lyapunov function, we provide a unified criterion for piecewise exponential stabilizability in terms of multiple linear co-positive Lyapunov functions.

Suggested Citation

  • Ding, Xiuyong & Liu, Xiu, 2017. "On stabilizability of switched positive linear systems under state-dependent switching," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 92-101.
    • Handle: RePEc:eee:apmaco:v:307:y:2017:i:c:p:92-101
    DOI: 10.1016/j.amc.2017.03.007
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    Cited by:

    1. Li, Yanan & Sun, Yuangong & Meng, Fanwei & Tian, Yazhou, 2018. "Exponential stabilization of switched time-varying systems with delays and disturbances," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 131-140.
    2. 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).
    3. Zhang, Jie & Sun, Yuangong, 2021. "Practical exponential stability of discrete-time switched linear positive systems with impulse and all modes unstable," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    4. Peng, Xiao & Wang, Yijing & Zuo, Zhiqiang, 2022. "Co-design of state-dependent switching law and control scheme for variable-order fractional nonlinear switched systems," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    5. 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).
    6. Ju, Yanhao & Sun, Yuangong & Meng, Fanwei, 2020. "Stabilization of switched positive system with impulse and marginally stable subsystems: A mode-dependent dwell time method," Applied Mathematics and Computation, Elsevier, vol. 383(C).

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