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.

中文翻译：

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使用依赖模态一致稳定函数的切换随机非线性系统的渐近稳定性分析

在本文中，我们打算研究一类时变切换随机非线性系统的概率均匀全局渐近稳定性（UGAS-P）。切换随机系统稳定性的常规标准基于李雅普诺夫函数的无穷小发生器的负性，证明这些标准是保守的。考虑到这一事实，在一致稳定函数 (USF) 的帮助下，作用于李雅普诺夫函数的每个活动子系统的无穷小生成器被放宽为不定的。随后，通过应用弱化条件和模态相关平均驻留时间 (MDADT) 技术，提出了渐近稳定性的改进标准。此外，还给出了数值例子来验证所得结果的有效性。