A SYNCHRONIZATION CONDITION FOR COUPLED NONLINEAR SYSTEMS WITH TIME-DELAY: A FREQUENCY DOMAIN APPROACH

This paper considers the synchronization problem for nonlinear systems with time-delay couplings. We assume that the error dynamics can be rewritten as a feedback connection of a linear delay system with multiple inputs and outputs and nonlinear elements which are decentralized and satisfy a sector condition. Then, we derive a synchronization condition for time-delay coupled systems by applying the multivariable circle criterion. Unlike the conventional synchronization criteria, the derived criterion is based on a frequency-domain stability condition and avoids the use of the Lyapunov-Krasovskii approach. As a result, the condition based on the circle criterion does not contain the conservativeness caused by the Lyapunov-Krasovskii approach. The effectiveness of the proposed criterion is shown by examples of coupled Chua systems with delay coupling.