Event-triggered synchronization for delayed dynamic complex networks via impulsive control strategy

This paper investigates the problem of event-triggered impulsive synchronization control for a class of hybrid delayed dynamical complex networks. Based on the Lyapunov function method, two control strategies—distributed event-triggered impulsive control and event-triggered pinning impulsive control—are proposed to guarantee synchronization of complex networks. The first strategy does not require prior knowledge of the network topology, thereby greatly reducing implementation difficulty. The second strategy controls only a subset of nodes in the network, which significantly reduces the consumption of control resources. Several sufficient conditions are established to reveal the potential relationships among the event-triggered mechanisms, control input, and impulsive action. In addition, the proposed event-triggered mechanisms can effectively exclude Zeno behavior. Finally, some numerical examples are provided to verify the effectiveness of the theoretical results for the synchronization of delayed dynamic complex networks.