Synchronization of Coupled Chaotic Systems with Time-delay

In this paper we consider the synchonization problem for four identical chaotic systems unidirectionally or bidirectionally coupled using state/output feedback with time-delays. Firstly, we show using the small-gain theorem that the trajectories of diffusively coupled strictly semi-dissipative systems converge to a bounded region. Then, for symmetric networks of identical systems, we show that the synchronization problem can be reduced to the stability problem of retarded systems