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Article

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

by
Zhiguo Yan
1,2 and
Fangxu Su
3,*
1
School of Control Science and Engineering, Shandong University, Jinan 250061, China
2
School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
3
School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(6), 979; https://doi.org/10.3390/math10060979
Submission received: 21 February 2022 / Revised: 10 March 2022 / Accepted: 15 March 2022 / Published: 18 March 2022
(This article belongs to the Special Issue Impulsive Control Systems and Complexity II)
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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.
Keywords: mean-square strong stability; Markov jump; discrete-time stochastic system; overshoot; output feedback mean-square strong stability; Markov jump; discrete-time stochastic system; overshoot; output feedback

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MDPI and ACS Style

Yan, Z.; Su, F. Mean-Square Strong Stability and Stabilization of Discrete-Time Markov Jump Systems with Multiplicative Noises. Mathematics 2022, 10, 979. https://doi.org/10.3390/math10060979

AMA Style

Yan Z, Su F. Mean-Square Strong Stability and Stabilization of Discrete-Time Markov Jump Systems with Multiplicative Noises. Mathematics. 2022; 10(6):979. https://doi.org/10.3390/math10060979

Chicago/Turabian Style

Yan, Zhiguo, and Fangxu Su. 2022. "Mean-Square Strong Stability and Stabilization of Discrete-Time Markov Jump Systems with Multiplicative Noises" Mathematics 10, no. 6: 979. https://doi.org/10.3390/math10060979

APA Style

Yan, Z., & Su, F. (2022). Mean-Square Strong Stability and Stabilization of Discrete-Time Markov Jump Systems with Multiplicative Noises. Mathematics, 10(6), 979. https://doi.org/10.3390/math10060979

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