A Synchronization Condition for Coupled Nonlinear Systems with Time-delay -A Circle Criterion Approach-*

This paper considers the synchronization problem for coupled chaotic systems with time-delay. We assume that the error dynamics can be rewritten by 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 coupled systems with delay by applying a multivariable circle criterion. Unlike the conventional synchronization criteria, the derived criterion is based on a frequency-domain condition and can avoid the use of the Lyapunov-Krasovskii approach. As a result, the condition 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.