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Mode-independent control of singular Markovian jump systems: A stochastic optimization viewpoint

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  • Wang, Guoliang

Abstract

In this paper, the mode-independent control problem of singular Markovian jump systems is firstly studied by exploiting a stochastic optimization viewpoint. A new kind of mode-independent H∞ controller satisfying a minimum variance approximation is constructed, whose gain is composed of some mode-dependent control gains. The available probability of system mode is described by the Bernoulli variable and taken into account. It shows that such a probability plays an important role in system analysis and associates mode-independent controller with mode-dependent controllers. When the probability is unknown, a kind of adaptive controller is proposed such that the resulting closed-loop system is robust stochastically admissible with an H∞ performance. All the proposed conditions are given in terms of linear matrix inequalities. Two numerical examples are used to demonstrate the effectiveness of the proposed methods.

Suggested Citation

  • Wang, Guoliang, 2016. "Mode-independent control of singular Markovian jump systems: A stochastic optimization viewpoint," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 155-170.
    • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:155-170
    DOI: 10.1016/j.amc.2016.04.004
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    References listed on IDEAS

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    1. Wang, Guoliang & Zhang, Qingling & Yang, Chunyu & Su, Chengli, 2015. "Stabilization of continuous-time randomly switched systems via the LMI approach," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 527-538.
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    Cited by:

    1. Wang, Guoliang & Zhu, Zhikang & Zhang, Yande, 2024. "Stabilization of continuous-time Markovian jump systems: A mode separation but optimization method," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    2. Feng, Bo & Feng, Zhiguang & Li, Peng, 2023. "Improved results on reachable set synthesis of Markovian jump systems with time-varying delays: General asynchronous control approaches," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    3. 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).
    4. 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.
    5. Wang, Guoliang & Li, Zhiqiang & Zhang, Qingling & Yang, Chunyu, 2017. "Robust finite-time stability and stabilization of uncertain Markovian jump systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 377-393.
    6. Tian, Yufeng & Wang, Yuzhong & Ren, Junchao, 2020. "Stability analysis and control design of singular Markovian jump systems via a parameter-dependent reciprocally convex matrix inequality," Applied Mathematics and Computation, Elsevier, vol. 386(C).

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