Finite time stability of stochastic nonlinear systems with state‐dependent delayed impulses and its applications in Cohen–Grossberg neural network

Abstract This paper studies the finite time stability (FTS) and finite time contractive stability (FTCS) for stochastic impulsive systems, where the impulse is related to the delayed state and the delay is state‐dependent. By utilizing the stochastic analysis and the Lyapunov theory, we establish several FTS and FTCS criteria, respectively, involving stabilizing impulses and destabilizing impulses. The proposed criteria are constructive and amenable to verification for practical systems. To demonstrate applicability, we apply the results to the stabilization problem of a Cohen–Grossberg impulsive neural network with state‐dependent delays, and corroborate the theoretical findings through a numerical example.