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This article is devoted to solving the problem of stochastically weakly locally exponential stability of switched stochastic systems with the state-dependent delay. Different from the previous works, we introduce the state-dependent delay, which is a random variable dependent on the system state so that the bound of the delay is unknown. In addition, we also consider the influence of switching on the stability of the system. By using multiple Lyapunov–Krasovskii functionals and some novel stochastic analysis techniques, we obtain sufficient conditions for stochastically weakly locally exponential stability of the hybrid system. Two examples are provided to verify the correctness of the proposed results.
Fan et al. (Thu,) studied this question.