This paper concerns the synchronization of time-delayed systems with periodic on-off coupling. Based on the stability theory and the comparison theorem of time-delayed differential equations, sufficient conditions for complete synchronization of systems with constant delay and time-varying delay are established. Compared with the results based on the Krasovskii-Lyapunov method, the sufficient conditions established in this paper are less restrictive. The theoretical results show that two time-delayed systems can achieve complete synchronization when the average coupling strength is sufficiently large. Numeric evidence shows that the synchronization speed depends on the coupling strength, on-off rate and time delay.
time-delayed system, complete synchronization, discontinuous coupling