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Stability, l1-gain and l∞-gain analysis for discrete-time positive switched singular delayed systems

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  • Li, Shuo
  • Xiang, Zhengrong

Abstract

In this paper, the problems of stability, l1-gain and l∞-gain analysis for positive switched singular systems with time delay are addressed. Both l1-gain and l∞-gain performance are analyzed. Firstly, a necessary and sufficient condition of positivity for the system is established by using the singular value decomposition method. Then by introducing new state vectors, the positive switched singular system is transformed into a standard positive switched system, and sufficient conditions for the positive switched singular delayed system to be asymptotically stable with an l1-gain performance and an l∞-gain performance are obtained, respectively. Finally, three numerical examples are presented to demonstrate the proposed results.

Suggested Citation

  • Li, Shuo & Xiang, Zhengrong, 2016. "Stability, l1-gain and l∞-gain analysis for discrete-time positive switched singular delayed systems," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 95-106.
    • Handle: RePEc:eee:apmaco:v:275:y:2016:i:c:p:95-106
    DOI: 10.1016/j.amc.2015.11.053
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    References listed on IDEAS

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    1. Lixian Zhang & Peng Shi, 2011. "filtering for a class of switched linear parameter varying systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(5), pages 781-788.
    2. 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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    Cited by:

    1. Xie, Jiyang & Zhu, Shuqian & Feng, Jun-e, 2020. "Delay-dependent and decay-rate-dependent conditions for exponential mean stability and non-fragile controller design of positive Markov jump linear systems with time-delay," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    2. Kwak, Dohyeok & Kim, Jung Hoon & Hagiwara, Tomomichi, 2023. "Generalized framework for computing the L∞-induced norm of sampled-data systems," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    3. Fu, Lei & Ma, Yuechao, 2016. "Passive control for singular time-delay system with actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 181-193.

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