Synchronization of coupled nonlinear systems with time delay

In this paper we consider synchronization of two identical nonlinear systems bidirectionally coupled with time-delay. Firstly, we show using the small-gain theorem that trajectories of coupled strictly semi-passive systems converge to a bounded region. Next, using this result, we derive a condition for synchronization of the systems by the Lyapunov-Krasovskii theorem. Finally we illustrate the effectiveness of the derived conditions with a numerical example.