This paper firstly discusses the existence and boundedness of unique global solution for highly nonlinear switched stochastic systems (SSSs) with time delays, where the switching signal is deterministic switching signal. Although the existence and boundedness of unique global solution can be obtained under local Lipschitz condition and Khasminskii‐type condition, highly nonlinear SSSs with time delays may not be stable. Therefore, a delay feedback control function can be designed for studying the stability of highly nonlinear SSSs with time delays, whose coefficients do not satisfy the linear growth condition. By using the Mathematical induction, Lyapunov function approach and the average dwell time method, H_∞ stability and the pth moment exponential stability are studied for highly nonlinear SSSs with time delays. An explanatory example is given to illustrate the effectiveness of the main results.

中文翻译：

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具有时滞的高度非线性切换随机系统的延迟反馈控制镇定

本文首先讨论具有时滞的高度非线性切换随机系统（SSS）的唯一全局解的存在性和有界性，其中切换信号为确定性切换信号。尽管可以在局部Lipschitz条件和Khasminskii型条件下获得唯一全局解的存在性和有界性，但是具有时滞的高度非线性SSS可能不稳定。因此，可以设计一个延迟反馈控制函数来研究具有时间延迟且其系数不满足线性增长条件的高度非线性SSS的稳定性。通过使用数学归纳法，Lyapunov函数的方法，并且平均停留时间的方法，ħ _∞稳定性和p研究了具有时滞的高度非线性SSS的矩矩指数稳定性。给出了一个解释性例子来说明主要结果的有效性。