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Practical stability of switched homogeneous positive nonlinear systems: Max-separable Lyapunov function method

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  • Liang, Mengqian
  • Tian, Yazhou

Abstract

The practical stability problem of switched homogeneous positive nonlinear systems (SHPNS) is addressed in this study, which includes two instances in terms of continuous-time and discrete-time. Sufficient conditions are presented by using the max-separable Lyapunov function (MSLF) approach, such that each solution of SHPNS is practically stable. The distinction between the existing results and the obtained results is that ours are not only relatively concise but also easily verifiable, and the theoretical results are also extended to a more general case without restricting the systems to be positive. Eventually, a pair of examples are proposed to explain the approach’s validity.

Suggested Citation

  • Liang, Mengqian & Tian, Yazhou, 2022. "Practical stability of switched homogeneous positive nonlinear systems: Max-separable Lyapunov function method," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    • Handle: RePEc:eee:apmaco:v:428:y:2022:i:c:s0096300322002648
    DOI: 10.1016/j.amc.2022.127190
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    References listed on IDEAS

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    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. 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).
    3. Sun, Yuangong & Tian, Yazhou, 2022. "Polynomial stability of positive switching homogeneous systems with different degrees," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    4. Jun Cheng & Hong Zhu & Shouming Zhong & Yuping Zhang, 2012. "Robust Stability of Switched Delay Systems with Average Dwell Time under Asynchronous Switching," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, October.
    5. Shuo Li & Zhengrong Xiang, 2017. "Stabilisation of a class of positive switched nonlinear systems under asynchronous switching," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(7), pages 1537-1547, May.
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    Cited by:

    1. 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).

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