Graph-Dependent Sufficient Conditions for Synchronization ofNetwork Coupled System With Time-delay

This paper studies the synchronization of network coupled systems consisting of many identical dynamic subsystems as well as network coupling with interaction time-delay. Based on graph theory and Lyapunov stability theory, the paper gives two sufficient conditions for the total system synchronization with respect to the graph structures of network coupling interaction, one is delay-independent and the other is the delay-dependent. These two conditions are compared with Wu's research, which was established without taking interaction time-delays into account. Simulations with two examples show the influences of the interaction timedelay as well as graph structures on the overall synchronization of subsystems.