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Stability analysis and control design of singular Markovian jump systems via a parameter-dependent reciprocally convex matrix inequality

Author

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  • Tian, Yufeng
  • Wang, Yuzhong
  • Ren, Junchao

Abstract

This paper is concerned with the problems of stochastic stability and control design for singular Markovian jump systems (SMJSs) with time varying delay. The derivative coefficient is considered to be mode dependent. A parameter-dependent reciprocally convex matrix inequality (PDRCMI) is constructed, which covers some existing ones as its special cases. Different from some existing ones, the introduced parameters are completely known, which can be optimized by an iteration algorithm. To decrease the redundant decision variables, a mild assumption is given for the case of mode-dependent coefficient such that the considered system is decomposed into differential equations and algebraic ones. In this case, the components of state vectors of the subsystem are applied to construct a new augmented Lyapunov-Krasovkii functional (LKF). Based on the PDRCI and the new augmented LKF, a novel stochastic stability condition with both less computational demands and less conservativeness is derived. Based on the decomposed subsystems and the stability condition, a set of state feedback controller is designed in terms of linear matrix inequalities (LMIs). Some numerical examples are introduced to illustrate the effectiveness of the proposed results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304306
    DOI: 10.1016/j.amc.2020.125471
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    References listed on IDEAS

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    1. 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.
    2. Ya-Li Zhi & Yong He & Jianhua Shen & Min Wu, 2018. "New stability criteria of singular systems with time-varying delay via free-matrix-based integral inequality," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(5), pages 1032-1039, April.
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    Cited by:

    1. Fu, Xiuwen & Sheng, Zhaoliang & Lin, Chong & Chen, Bing, 2022. "New results on admissibility and dissipativity analysis of descriptor time-delay systems," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    2. 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).
    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. Zhang, Jianan & Ma, Yuechao, 2023. "Adaptive fault-tolerant double asynchronous control for switched semi-Markov jump systems via improved memory sampled-data technique," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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