Synchronization of Nonlinear Coupled Delayed Networks via Intermittent Pinning Control: An Average Technique

This paper is concerned with the aperiodically intermittent pinning control (AIPC) for the synchronization of nonlinear coupled networks, where both the internal time delay and the coupling time delay are considered. We consider the aperiodicity of AIPC from the average sense. Then by extending the Halanay's inequality to the case with two kinds different delays, we obtain two kinds of synchronization criteria: one is the upper bound of time delay must be less than the average control width but can be larger than certain control widths; the other is that the upper bound of time delay has no relationship with the average control width. We show that the two criteria lead to complementary results. The effectiveness of our results is confirmed by numerical simulations.