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Positivity, exponential stability and disturbance attenuation performance for singular switched positive systems with time-varying distributed delays

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  • Li, Shuo
  • Xiang, Zhengrong

Abstract

This article analyzes the singular switched positive systems with time-varying distributed delays from the perspective of positivity, exponential stability and disturbance attenuation performance referring to both L1-gain and L∞-gain. For the system, a sufficient and necessary positivity condition is firstly developed by using the singular value decomposition technique. Then, a sufficient condition of exponential stability, which makes the considered system exponentially stable, is proposed on the basis of co-positive Lyapunov–Krasovskii functional and average dwell time techniques, and the obtained exponential decay rate can be adjusted in the light of various actual situations. Furthermore, the article analyzes the disturbance attenuation performance referring to both L1-gain and L∞-gain, and through the convex optimization approach, the optimal L1-gain and L∞-gain performance level could be established, respectively. Three examples are finally presented to show the feasibility and effectiveness of the obtained results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:372:y:2020:i:c:s0096300319309737
    DOI: 10.1016/j.amc.2019.124981
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    References listed on IDEAS

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    1. 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.
    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.
    3. Qi, Wenhai & Zong, Guangdeng & Cheng, Jun & Jiao, Ticao, 2019. "Robust finite-time stabilization for positive delayed semi-Markovian switching systems," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 139-152.
    4. Wang, Zhichuang & Chen, Guoliang & Ba, Hezhen, 2019. "Stability analysis of nonlinear switched systems with sampled-data controllers," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 297-309.
    5. Chen, Xiaoming & Chen, Mou & Qi, Wenhai & Shen, Jun, 2016. "Dynamic output-feedback control for continuous-time interval positive systems under L1 performance," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 48-59.
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    Cited by:

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    2. Liu, Jason J.R. & Lam, James & Wang, Xiaomei & Kwok, Ka-Wai, 2023. "Non-fragile PD control of linear time-delay positive discrete-time systems," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    3. Wang, Zhe & Xue, Dingyu & Pan, Feng, 2021. "Observer-based robust control for singular switched fractional order systems subject to actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    4. 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).
    5. Li, Jinghan & Zhao, Jun, 2022. "Bumpless transfer based event-triggered control for switched linear systems with state-dependent switching," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    6. 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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