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Mean-Square Strong Stability and Stabilization of Discrete-Time Markov Jump Systems with Multiplicative Noises

Author

Listed:
  • Zhiguo Yan

    (School of Control Science and Engineering, Shandong University, Jinan 250061, China
    School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Fangxu Su

    (School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

Abstract

In this paper, the mean-square strong stability and stabilization of discrete-time Markov jump systems are studied. Firstly, the definition of mean-square strong stability is given, and the necessary and sufficient conditions for mean-square strong stability are derived. Secondly, several necessary and sufficient conditions for mean-square strong stabilization via a state feedback controller and an output feedback controller are obtained. Furthermore, explicit expressions for the state feedback controller and static output feedback controller are obtained. Finally, two examples are given to illustrate the validity of the above results.

Suggested Citation

  • Zhiguo Yan & Fangxu Su, 2022. "Mean-Square Strong Stability and Stabilization of Discrete-Time Markov Jump Systems with Multiplicative Noises," Mathematics, MDPI, vol. 10(6), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:979-:d:774313
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    References listed on IDEAS

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    1. Peng, Dongxue & Li, Xiaodi & Rakkiyappan, R. & Ding, Yanhui, 2021. "Stabilization of stochastic delayed systems: Event-triggered impulsive control," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    2. Zhao, Yongshun & Li, Xiaodi & Cao, Jinde, 2020. "Global exponential stability for impulsive systems with infinite distributed delay based on flexible impulse frequency," Applied Mathematics and Computation, Elsevier, vol. 386(C).
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