This paper deals with stochastically globally exponential stability (SGES) for stochastic impulsive differential systems (SIDSs) with discrete delays (DDs) and infinite distributed delays (IDDs). By using vector Lyapunov function (VLF) and average dwell-time (ADT) condition, we investigate the unstable impulsive dynamics and stable impulsive dynamics of the suggested system, and some novel stability criteria are obtained for SIDSs with DDs and IDDs. Moreover, our results allow the discrete delay term to be coupled with the nondelay term, and the infinite distributed delay term to be coupled with the nondelay term. Finally, two examples are given to verify the effectiveness of our theories.

中文翻译：

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向量Lyapunov函数的离散无限分布时滞随机脉冲微分系统的随机全局指数稳定性。

本文研究具有离散延迟（DDs）和无限分布延迟（IDDs）的随机脉冲差分系统（SIDS）的随机全局指数稳定性（SGES）。通过使用向量李雅普诺夫函数（VLF）和平均停留时间（ADT）条件，我们研究了所建议系统的不稳定脉冲动力学和稳定脉冲动力学，并为具有DDs和IDD的SIDSs获得了一些新的稳定性准则。此外，我们的结果允许离散延迟项与非延迟项耦合，而无限分布式延迟项与非延迟项耦合。最后，给出两个例子来验证我们理论的有效性。