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Dynamic event-based mixed H∞ and dissipative asynchronous control for Markov jump singularly perturbed systems

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  • Wang, Yanqian
  • Chen, Fu
  • Zhuang, Guangming
  • Yang, Guang

Abstract

The paper investigates the issue of mixed H∞ and dissipative asynchronous controller design for a class of Markov jump singularly perturbed systems (MJSPSs). A suitable dynamic event-triggered rule is offered to further mitigate the transmission burden of communication network. Since the mode information of Markov chain is extremely difficult to get, an asynchronous controller is well constructed. Hence, a hidden Markov model (HMM) is chosen to describe the non-synchronous facts between states of the original Markov chain and the constructed non-synchronous controller. Resorting to the Lyapunov functional concerning the internal dynamic variable, sufficient conditions of stochastically stable with a certain mixed H∞ and dissipative performance for the resulting closed-loop MJSPSs are offered. Based on the LMI technique, the design framework of asynchronous controller and the dynamic event-triggered rule are given in a unified way. Lastly, a modified DC motor model is offered to demonstrate the superiority of the proffered method.

Suggested Citation

  • Wang, Yanqian & Chen, Fu & Zhuang, Guangming & Yang, Guang, 2020. "Dynamic event-based mixed H∞ and dissipative asynchronous control for Markov jump singularly perturbed systems," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304045
    DOI: 10.1016/j.amc.2020.125443
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    References listed on IDEAS

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    4. Zhuang, Guangming & Xu, Shengyuan & Xia, Jianwei & Ma, Qian & Zhang, Zhengqiang, 2019. "Non-fragile delay feedback control for neutral stochastic Markovian jump systems with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 21-32.
    5. Yanqian Wang & Guangming Zhuang & Fu Chen, 2020. "A dynamic event-triggered H∞ control for singular Markov jump systems with redundant channels," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(1), pages 158-179, January.
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    Cited by:

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    12. Wang, Haitao & Chen, Xiangyong & Wang, Jing, 2022. "H∞ sliding mode control for PDT-switched nonlinear systems under the dynamic event-triggered mechanism," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    13. Fan, Yanyan & Jin, Zhenlin & Luo, Xiaoyuan & Guo, Baosu, 2022. "Robust finite-time consensus control for Euler–Lagrange multi-agent systems subject to switching topologies and uncertainties," Applied Mathematics and Computation, Elsevier, vol. 432(C).
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