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H∞ control for singular Markovian jump systems with incomplete knowledge of transition probabilities

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  • Kwon, Nam Kyu
  • Park, In Seok
  • Park, PooGyeon

Abstract

This paper proposes a H∞ state-feedback control for singular Markovian jump systems with incomplete knowledge of transition probabilities. Different from the previous results where the transition rates are completely known or the bounds of the unknown transition rates are given, a more general situation where the transition rates are partly unknown and the bounds of the unknown transition rates are also unknown is considered. Moreover, in contrast to the singular Markovian jump systems studied recently, the proposed method does not require any tuning parameters that arise when handling non-convex terms related to the mode-dependent Lyapunov matrices and the corresponding self-mode transition rates. Also, this paper uses all possible slack variables related to the transition rates into the relaxation process which contributes to reduce the conservatism. Finally, two numerical examples are provided to demonstrate the performance of H∞ mode-dependent control.

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  • 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.
    • Handle: RePEc:eee:apmaco:v:295:y:2017:i:c:p:126-135
    DOI: 10.1016/j.amc.2016.09.004
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    References listed on IDEAS

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    1. Wang, Guoliang, 2015. "Stochastic stabilization of singular systems with Markovian switchings," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 390-401.
    2. Wang, Jimin & Ma, Shuping & Zhang, Chenghui, 2016. "Stability analysis and stabilization for nonlinear continuous-time descriptor semi-Markov jump systems," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 90-102.
    3. Shen, Mouquan & Yan, Shen & Zhang, Guangming & Park, Ju H., 2016. "Finite-time H∞ static output control of Markov jump systems with an auxiliary approach," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 553-561.
    4. 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.
    5. Ma, Yuechao & Jia, Xiaorui & Liu, Deyou, 2016. "Robust finite-time H∞ control for discrete-time singular Markovian jump systems with time-varying delay and actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 213-227.
    6. Chen, Mengshen & Yang, Xiaofei & Shen, Hao & Yao, Fengqi, 2016. "Finite-time asynchronous H∞ control for Markov jump repeated scalar non-linear systems with input constraints," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 172-180.
    7. Jiang, Baoping & Gao, Cunchen & Xie, Jing, 2015. "Passivity based sliding mode control of uncertain singular Markovian jump systems with time-varying delay and nonlinear perturbations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 187-200.
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    Cited by:

    1. Wang, Guoliang & Cai, Hongyang & Zhang, Qingling & Yang, Chunyu, 2017. "Stabilization of stochastic delay systems via a disordered controller," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 98-109.
    2. 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.
    3. Xu, Qiyi & Zhang, Yijun & Qi, Wenhai & Xiao, Shunyuan, 2020. "Event-triggered mixed H∞ and passive filtering for discrete-time networked singular Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    4. Haghighi, Payam & Tavassoli, Babak & Farhadi, Alireza, 2020. "A practical approach to networked control design for robust H∞ performance in the presence of uncertainties in both communication and system," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    5. Gao, Xianwen & He, Hangfeng & Qi, Wenhai, 2017. "Admissibility analysis for discrete-time singular Markov jump systems with asynchronous switching," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 431-441.
    6. Hyun Kim, Sung, 2019. "Generalized relaxation techniques for robust H∞ filtering of nonhomogeneous Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 542-556.
    7. 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).

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