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Asynchronous H∞ control for hidden singular Markov jump systems with incomplete transition probabilities via state decomposition approach

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  • Zhao, Yinghong
  • Ma, Yuechao

Abstract

This paper addresses the asynchronous H∞ control problem for hidden singular Markov jump systems (HSMJSs) with incomplete transition probabilities. By employing the state decomposition approach, a novel augmented Lyapunov-Krasovkii functional (LKF) with the components of state vectors is designed to reduce the redundant decision variables. Meanwhile, a parameter-dependent reciprocally convex matrix inequality (PDRCMI) is introduced to decrease conservatism. To handle the non-synchronization phenomenon of the system mode and the controller mode, an asynchronous state feedback controller based on hidden Markov model (HMM) is developed. In addition, the incomplete transition probabilities are considered so that a more practical potential strategy is addressed. Finally, numerical examples are provided to illustrate the superiority and practicability of the presented results.

Suggested Citation

  • Zhao, Yinghong & Ma, Yuechao, 2021. "Asynchronous H∞ control for hidden singular Markov jump systems with incomplete transition probabilities via state decomposition approach," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    • Handle: RePEc:eee:apmaco:v:407:y:2021:i:c:s0096300321003933
    DOI: 10.1016/j.amc.2021.126304
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    References listed on IDEAS

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    1. Wang, Jing & Liang, Kun & Huang, Xia & Wang, Zhen & Shen, Hao, 2018. "Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 247-262.
    2. Kong, Chuifeng & Ma, Yuechao & Liu, Deyou, 2019. "Observer-based quantized sliding mode dissipative control for singular semi-Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
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    12. Kwon, Nam Kyu & Park, In Seok & Park, PooGyeon, 2017. "H∞ control for singular Markovian jump systems with incomplete knowledge of transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 126-135.
    13. Yan, Zhiguo & Song, Yunxia & Liu, Xiaoping, 2018. "Finite-time stability and stabilization for Itô-type stochastic Markovian jump systems with generally uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 512-525.
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    3. Chen, Wenbin & Lu, Junwei & Zhuang, Guangming & Gao, Fang & Zhang, Zhengqiang & Xu, Shengyuan, 2022. "Further results on stabilization for neutral singular Markovian jump systems with mixed interval time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 420(C).

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