Abstract
In this paper, we intend to investigate uniform global asymptotic stability in probability (UGAS-P) for a class of time-varying switched stochastic nonlinear systems. Conventional criteria on stability for switched stochastic systems are based on the negativity of the infinitesimal generator of Lyapunov functions, it is demonstrated that these criteria are conservative. Taking this fact into account, the infinitesimal generator for each active subsystem acting on Lyapunov functions is relaxed to be indefinite with the help of uniformly stable function (USF). Subsequently, improved criteria on asymptotic stability are proposed by applying the weakened condition and mode-dependent average dwell time (MDADT) technique. In addition, numerical examples are presented to verify the effectiveness of the obtained results.
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Recommended by Associate Editor Ding Zhai under the direction of Editor Jessie (Ju H.) Park. This work was supported by the National Natural Science Foundation of China under Grants 61803324, 61803006 and 61803069.
Dianfeng Zhang received his Ph.D. degree in Control Science and Engineering, Dalian University of Technology, China, in 2017. He is currently a lecturer in the School of Mathematics and Information Science, Yantai University, China. His research interests include nonlinear control systems, stochastic dissipative systems and stochastic switched systems.
Yong-Feng Gao received his Ph.D. degree in Control Science and Engineering, Dalian University of Technology, China. He is currently a lecturer in the School of Control Science and Engineering, Dalian University of Technology. His research interests include event-triggering control and nonlinear control systems.
Sheng-Li Du received his Ph.D. degree in Control Theory and Control Engineering from the Dalian University of Technology, China, in 2016. From July 2016 to March 2017, he worked as a Research Assistant in the Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong. From March 2017 to August 2017, he worked as a Research Associate in the Department of Mathematics, City University of Hong Kong, Hong Kong. He joined Beijing University of Technology in August 2017. His research interests include switched systems and multiagent systems.
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Zhang, D., Gao, YF. & Du, SL. Asymptotic Stability Analysis for Switched Stochastic Nonlinear Systems Using Mode-dependent Uniformly Stable Functions. Int. J. Control Autom. Syst. 18, 2259–2267 (2020). https://doi.org/10.1007/s12555-019-0545-z
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DOI: https://doi.org/10.1007/s12555-019-0545-z