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Asymptotic Stability Analysis for Switched Stochastic Nonlinear Systems Using Mode-dependent Uniformly Stable Functions

Dianfeng Zhang, Yong-Feng Gao, and Sheng-Li Du*
International Journal of Control, Automation, and Systems, vol. 18, no. 9, pp.2259-2267, 2020

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 modedependent average dwell time (MDADT) technique. In addition, numerical examples are presented to verify the effectiveness of the obtained results.

Keyword : Asymptotic stability, mode-dependent average dwell time, switched stochastic nonlinear systems, uniformly stable function.

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