Fixed-time Lyapunov criteria of stochastic impulsive time-delay systems and its application to synchronization of Chua’s circuit networks

In this paper, we investigate the fixed-time stability and synchronization issues of stochastic impulsive delay complex networks (SICNs) with delayed impulses. Firstly, a new fixed-time stability criterion, which provides a direct connection between impulsive strength, impulsive instants, delays and the stability time, is established for stochastic delay systems with delayed impulsive. In this criterion, two types of delays: system delay and impulsive delay are considered, and the impulsive intensity at each impulse instant can be different, (facilitate or disrupt stability). It is the first time to consider the fixed-time stability issues of this case. Secondly, based on this criterion, a novel feedback controller and an adaptive controller are designed to study the fixed-time synchronization of SICNs with delayed impulses; Thirdly, by utilizing Lyapunov functional theory, stochastic analysis technique, matrix inequality analysis techniques and proposed stability criterion, the fixed-time synchronization conditions of SICNs, are derived in the form of linear matrix inequalities (LMIs). Finally, a numerical example and an application example, Chua’s circuit networks, are provided to illustrate the validity of the theoretical analysis.