Cluster Synchronization for Stochastic Coupling Delay Complex Networks via Event-Triggered Impulsive Control With Actuation Delay

This article investigates cluster synchronization for stochastic complex networks (SCNs) with coupling delay via event-triggered impulsive control (ETIC), which accounts for the actuation delay connecting the impulsive controller to the actuator, resulting in inconsistent triggering and impulsive activation time. First, by constructing an auxiliary function, network issues caused by coupling delay are effectively addressed. Second, under the support of Lyapunov–Razumihin (L-R) technique and the proposed auxiliary function, the condition for ensuring cluster synchronization of SCNs is proposed by using linear matrix inequalities (LMIs), and the Zeno behavior is eliminated. Finally, a numerical simulation example is presented to validate the effectiveness of the proposed theoretical results.