Global μ-synchronization for coupling delayed complex dynamical networks via event-triggered delayed impulsive control

Abstract

This paper mainly focuses on solving the global μ-synchronization issue of complex dynamical networks (CDNs) by a novel event-triggered impulsive control (ETIC) method with time delays. This method combines the advantages of impulsive control and event-triggered control and gets rid of the limitation that the Lyapunov function decreases strictly monotonically with the sequence of event triggers. An event-triggered mechanism is specifically designed to realize μ-synchronization for CDNs in this paper, which means that event-triggered control has been applied to μ-synchronization field for the first time. Compared with periodic impulsive control, ETIC only produces control effects when the event-triggered mechanism are met, which is more in line with the actual situation. By Lyapunov–Razumikhin, recursion, etc, some valid global μ-synchronization criteria of CDNs are obtained and also Zeno behavior is avoided. Additionally, coupled delays and uncertainties are considered in CDNs. Finally, two numerical examples are shown to demonstrate the correctness of the designed ETIC strategy.