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A common linear copositive Lyapunov function for switched positive linear systems with commutable subsystems

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  • Yanhui Tong
  • Lixian Zhang
  • Peng Shi
  • Changhong Wang

Abstract

This article is concerned with the existence problem of a common linear copositive Lyapunov function (CLCLF) for switched positive linear systems with stable and pairwise commutable subsystems. Three families of such systems composed of only continuous-time subsystems, only discrete-time subsystems and mixed continuous- and discrete-time subsystems are considered, respectively. It is demonstrated that a CLCLF can always be constructed for the underlying system whenever its subsystems are continuous-time, discrete-time or the mixed type. The case when the number of subsystems is two is first considered, then the obtained result is extended to the general case. Three numerical examples are given to verify the validity of the developed results.

Suggested Citation

  • Yanhui Tong & Lixian Zhang & Peng Shi & Changhong Wang, 2013. "A common linear copositive Lyapunov function for switched positive linear systems with commutable subsystems," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(11), pages 1994-2003.
    • Handle: RePEc:taf:tsysxx:v:44:y:2013:i:11:p:1994-2003
    DOI: 10.1080/00207721.2012.683830
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    Cited by:

    1. Chunbin Qin & Huaguang Zhang & Yanhong Luo & Binrui Wang, 2014. "Finite horizon optimal control of non-linear discrete-time switched systems using adaptive dynamic programming with ε-error bound," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(8), pages 1683-1693, August.
    2. Junfeng Zhang & Zhengzhi Han & Fubo Zhu, 2015. "-gain analysis and control synthesis of positive switched systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(12), pages 2111-2121, September.
    3. 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.
    4. Jun Shen & James Lam, 2015. "On ℓ and gains for positive systems with bounded time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(11), pages 1953-1960, August.

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