This paper investigates the stabilization problem for a class of nonlinear hybrid neutral stochastic differential equations (NSDEs) with different structural modes, employing a delay feedback control strategy. A key innovation lies in the consideration of non-differentiable delay functions, which are governed by significantly weaker assumptions and do not require a positive lower bound. By designing a mode-dependent delay feedback controller and constructing a novel Lyapunov functional with structural parameters, utilizing M-matrix theory and stochastic stability analysis, we derive sufficient conditions that guarantee the existence, uniqueness and boundedness of the global solution for the closed-loop system, along with exponential stability. A numerical example is provided to demonstrate that the proposed controller effectively stabilizes an otherwise unstable hybrid neutral stochastic delay system, thereby validating the efficacy of the control strategy.
Shen et al. (Tue,) studied this question.
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