Stability Analysis of Stochastic Delayed Differential Systems with State-Dependent-Delay Impulses: Application of Neural Networks

The previously studied stochastic delayed nonlinear systems with constant delayed or time-varying delayed impulsive controller, while we study stochastic delayed nonlinear systems under state-dependent-delayed impulsive controller. The difficulty is how to determine the time of impulses occurrence. Employing the Halanay differential inequality, Ito's formula, the average impulsive interval, impulsive control theory, comparison properties, several effective conditions ensuring stability of stochastic delayed nonlinear systems under state-dependent delayed impulsive controller are derived. This paper contributed to the stability analysis of delayed impulsive nonlinear systems with stochastic perturbation, which the impulsive involved delay is state dependent. We have developed exponential stability of delayed nonlinear systems with state-dependent-delay impulses and stochastic disturbance in this paper. In the future, more new methods should also be proposed. At the same time, we will consider the nonlinear systems with unbounded delays.