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On ℓ and gains for positive systems with bounded time-varying delays

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  • Jun Shen
  • James Lam

Abstract

This paper is devoted to the analysis of the ℓ∞ and L∞ gains for positive linear systems with interval time-varying delays. Through exploiting the monotonicity of the state trajectory, we first prove that for positive systems with constant delays, the ℓ∞ and L∞ gains are fully governed by the system matrices but independent of the delay size. Moreover, for positive systems with bounded time-varying delays, by comparing with the nominal systems with constant delays, it turns out that the ℓ∞ and L∞ gains are exactly the same as that of the constant delay systems. The results in this paper reveal that the ℓ∞ and L∞ gains of positive linear systems are not sensitive to the magnitude of time delays and hence the computation of ℓ∞ and L∞ gains of positive systems with bounded time-varying delays can be reduced to computing the ℓ∞ and L∞ gains of the corresponding delay-free systems. Both continuous-time and discrete-time cases are considered in this paper.

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  • 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.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:11:p:1953-1960
    DOI: 10.1080/00207721.2013.843217
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Li, Shuo & Xiang, Zhengrong, 2020. "Positivity, exponential stability and disturbance attenuation performance for singular switched positive systems with time-varying distributed delays," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    2. 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.

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