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Stochastic stabilization of singular systems with Markovian switchings

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  • Wang, Guoliang

Abstract

This paper studies the stochastic stabilization problem for a class of singular Markovian jump system. The aim is to determine whether or not there is a stochastic feedback controller stabilizing a given singular Markovian jump system (SMJS). A new kind of stochastic controller only in the diffusion part is proposed such that the closed-loop system has a unique solution and is almost surely exponentially admissible. New sufficient condition for the existence of such a controller is given as linear matrix inequalities (LMIs). Based on this, more extensions to transition probability matrix (TPM) with elements partially unknown and system states partially observable are developed. A numerical example is used to demonstrate the effectiveness of the proposed methods.

Suggested Citation

  • Wang, Guoliang, 2015. "Stochastic stabilization of singular systems with Markovian switchings," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 390-401.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:390-401
    DOI: 10.1016/j.amc.2014.11.019
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    Cited by:

    1. Sakthivel, R. & Saravanakumar, T. & Kaviarasan, B. & Marshal Anthoni, S., 2016. "Dissipativity based repetitive control for switched stochastic dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 340-353.
    2. 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.
    3. 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).
    4. Fang, Jiankang & Ren, Chengcheng & Wang, Hai & Stojanovic, Vladimir & He, Shuping, 2024. "Finite-region asynchronous H∞ filtering for 2-D Markov jump systems in Roesser model," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    5. 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.
    6. Fu, Lei & Ma, Yuechao, 2016. "Passive control for singular time-delay system with actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 181-193.

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