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Stability and stabilization for positive systems with semi-Markov switching

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  • Wang, Huajian
  • Qi, Wenhai
  • Zhang, Lihua
  • Cheng, Jun
  • Kao, Yonggui

Abstract

In this article, the problems of mean stability analysis and control synthesis are studied for stochastic switching systems subject to positive constraint. Such a switching is governed by a semi-Markov process subject to a special non-exponential distribution. Considering a linear Lyapunov-Krasovskii function (LKF), necessary and sufficient conditions are proposed to realize mean stability for the open-loop system. Based on this, the solvability conditions for the desired stabilizing controller can be determined under a linear programming (LP) framework. Finally, the theoretical findings are illustrated by the virus mutation treatment model.

Suggested Citation

  • Wang, Huajian & Qi, Wenhai & Zhang, Lihua & Cheng, Jun & Kao, Yonggui, 2020. "Stability and stabilization for positive systems with semi-Markov switching," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    • Handle: RePEc:eee:apmaco:v:379:y:2020:i:c:s0096300320302216
    DOI: 10.1016/j.amc.2020.125252
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    References listed on IDEAS

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    1. 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.
    2. Wang, Ruihua & Jiao, Ticao & Zhang, Tao & Fei, Shumin, 2019. "Improved stability results for discrete-time switched systems: A multiple piecewise convex Lyapunov function approach," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 54-65.
    3. Shuo Li & Zhengrong Xiang & Jian Guo, 2018. "Stabilisation for positive switched T-S fuzzy delayed systems under standard L1 and L∞ performance," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(6), pages 1226-1241, April.
    4. Qi, Wenhai & Gao, Xianwen, 2016. "H∞ observer design for stochastic time-delayed systems with Markovian switching under partly known transition rates and actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 80-97.
    5. Wenhai Qi & Yonggui Kao & Xianwen Gao, 2017. "Further results on finite-time stabilisation for stochastic Markovian jump systems with time-varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(14), pages 2967-2975, October.
    6. Wenhai Qi & Xianwen Gao, 2016. "Finite-time H-infinite control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(2), pages 1-1, January.
    7. Wenhai Qi & Xianwen Gao, 2016. "Finite-time control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(2), pages 500-508, January.
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    Cited by:

    1. Vargas, Alessandro N. & Caruntu, Constantin F. & Ishihara, João Y. & Bouzahir, Hassane, 2022. "Stochastic stability of switching linear systems with application to an automotive powertrain model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 278-287.
    2. 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).

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