Synchronization of directed complex dynamical networks based on distributed event-triggered communications

This paper studies the problem of synchronization on a complex dynamical network where the nodes' dynamics are nonlinear time-invariant systems and share a directed communication network. Firstly, we study the problem of synchronization on a directed network with physical links. An explicit Lyapunov function is constructed by using an appropriate matrix to derive the threshold of event generator. Then, the centralized event-triggered rule is achieved by using the set stability theory. Based on the centralized event-triggered rule, the distributed one is proposed to synchronize the directed complex network. The threshold of each event generator is composed of each node's states rather than neighboring node's. Finally, a numerical example is given to validate the correctness of the proposed synchronization criteria based on distributed event-triggered communication.