SIAM Journal on Control and Optimization, Volume 59, Issue 3, Page 2068-2092, January 2021.
This paper studies stability of stochastic impulsive switched systems with deterministic state-dependent impulses and switches. Here, “deterministic state-dependent” means that both switching and impulsive rules are deterministic and related to system states. Since impulses and switches are not necessarily synchronous, we first investigate stochastic impulsive switched systems with asynchronous time-dependent impulses and switches. Both the existence and convergence of the system solution are studied, and stability conditions are derived via the tradeoff between two average dwell-times for switching and impulsive time sequences. For the state-dependent case, based on active regions for the switching and assigned regions for the impulses, we first develop impulsive and switching rules such that both impulsive and switching times are stopping times, then verify the existence and uniqueness of the system solution, and finally establish stability conditions. Furthermore, we discuss the combination of time-dependent and state-dependent cases, and investigate the quasi solution of the system to relax the assumption on active regions. Finally, two numerical examples are presented to illustrate the derived results.

中文翻译：

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具有确定性状态相关脉冲和开关的随机脉冲开关系统的稳定性分析

SIAM Journal on Control and Optimization，第 59 卷，第 3 期，第 2068-2092 页，2021 年 1 月。
本文研究了具有确定性状态相关脉冲和开关的随机脉冲开关系统的稳定性。这里，“确定性状态相关”意味着切换和脉冲规则都是确定性的并且与系统状态相关。由于脉冲和开关不一定是同步的，我们首先研究具有异步时间相关脉冲和开关的随机脉冲开关系统。研究了系统解的存在性和收敛性，并通过切换和脉冲时间序列的两个平均驻留时间之间的权衡推导出稳定性条件。对于状态相关的情况，基于开关的活动区域和脉冲的指定区域，我们首先开发脉冲和开关规则，使得脉冲和开关时间都是停止时间，然后验证系统解的存在唯一性，最后建立稳定性条件。此外，我们讨论了时间依赖和状态依赖情况的组合，并研究了系统的准解以放宽对活动区域的假设。最后，给出了两个数值例子来说明推导出的结果。