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Dual approach to stability and stabilisation of uncertain switched positive systems

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  • Junfeng Zhang
  • Xudong Zhao
  • Ridong Zhang
  • Shaosheng Zhou

Abstract

This paper addresses two kinds of dual approaches to stability and stabilisation of uncertain switched positive systems under arbitrary switching and average dwell-time switching, respectively. The uncertainties in systems refer to polytopic ones. A new parameter-dependent switched linear copositive Lyapunov function is first proposed for uncertain switched positive systems. By using the new Lyapunov function associated with arbitrary switching and average dwell-time switching, respectively, sufficient conditions for the stability of the systems are established. Two alternative stability criteria based on two kinds of dual approaches are addressed. It is shown that the alternative criteria hold for not only the primal switched positive system but also its dual system. Then, the stabilisation of primal and dual switched positive systems under arbitrary switching and average dwell-time switching is solved, respectively. All present conditions are solvable in terms of linear programming. By some comparisons with existing results, the less conservativeness of the obtained results is verified. Finally, a practical example is provided to illustrate the effectiveness of the theoretical findings.

Suggested Citation

  • Junfeng Zhang & Xudong Zhao & Ridong Zhang & Shaosheng Zhou, 2017. "Dual approach to stability and stabilisation of uncertain switched positive systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 873-884, March.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:4:p:873-884
    DOI: 10.1080/00207721.2016.1224954
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    Cited by:

    1. Deng, Yalin & Zhang, Huasheng & Dai, Yuzhen & Li, Yuanen, 2022. "Interval stability/stabilization for linear stochastic switched systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 428(C).

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