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Synchronization of nonlinear oscillators by bidirectional diffusive coupling with time delay

In this paper we consider synchronization of two identical nonlinear systems bidirectionally coupled by a diffusive coupling with time-delay. Firstly, we show using the small-gain theorem that trajectories of any 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.