Finite-time stability and stabilization of linear discrete time-varying stochastic systems |
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| Authors: | Tianliang Zhang Feiqi Deng Weihai Zhang |
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| Institution: | 1. School of Automation Science and Engineering, South China University of Technology, Guangzhou, Guangdong 510640, PR China;2. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, Shandong 266590, PR China |
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| Abstract: | This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for the finite-time stability are presented via a state transition matrix approach. Secondly, this paper also develops the Lyapunov function method to study the finite-time stability and stabilization of discrete time-varying stochastic systems based on matrix inequalities and linear matrix inequalities (LMIs) so as to Matlab LMI Toolbox can be used.The state transition matrix-based approach to study the finite-time stability of linear discrete time-varying stochastic systems is novel, and its advantage is that the state transition matrix can make full use of the system parameter informations, which can lead to less conservative results. We also use the Lyapunov function method to discuss the finite-time stability and stabilization, which is convenient to be used in practical computations. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results. |
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| Keywords: | Corresponding author |
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