Structured stabilization of superlinear neutral stochastic systems by delay feedback control

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.