Stability of stochastic state-dependent delayed complex networks under stochastic hybrid impulsive control

In this paper, stability for state-dependent delayed complex networks under stochastic hybrid impulsive control is investigated. The impulses herein are stochastic and hybrid, that is, the impulsive gain at different impulsive moments is a sequence of random variables. The novel concept of average stochastic impulsive gain is proposed in this paper to deal with stochastic hybrid impulses. We also establish a new stochastic impulsive differential inequality with state-dependent delay. In the proceeding, combining the inequality with graph theory, stochastic analysis techniques and the Lyapunov method, stability criteria for the investigated networks are given. At the end, we apply the derived theoretical results to the special case of neural networks and the numerical analysis results illustrate the validity of the theoretical results.