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The stability of stochastic nonlinear systems with time-delay and state-dependent switching is studied in this paper. Firstly, system maximal solution is constructed and further extended as the global solution under certain mild conditions. Secondly, several Krasovskii-type stability and Razumikhin-type theorems are proposed by uniformly asymptotically stable functions (UASFs). These stability criteria overcome some stringent constraints associated with Lyapunov functional/functions. Finally, the theoretical findings are validated through two simulation examples.
Yao et al. (Wed,) studied this question.