Synchronization of dynamical networks with distributed event-based communication

In this paper, we study synchronization of a dynamical network whose nodes are linear time-invariant systems and are interconnected through a shared communication network. Firstly, synchronization of a dynamical network with physical links and undirected topology is reinvestigated from a set stability point of view. An explicit Lyapunov function with respect to its synchronization manifold is constructed for such a network by using properties of undirected networks. Based on this Lyapunov function, a distributed event-triggered sampling scheme is designed which decides when a node should send its sampled state to its neighbors across the communication network in order to achieve asymptotic synchronization of a dynamical network with communication links. The proposed triggering rule only depends on the state of the node itself and the sampled ones that are received from its neighbors.