Local Synchronization for Delayed Complex Dynamical Networks via Self-Triggered Impulsive Control Involving Delays.

This article investigates the local synchronization for delayed complex dynamical networks (CDNs) under self-triggered impulsive control (STIC) approaches involving delays. With the help of Lyapunov-Razumikhin methods and comparison principle, some design criteria of STIC strategies ensuring local synchronization for delayed CDNs with delayed impulses are provided, and Zeno behavior can be avoided. Compared with the existing results on synchronization of CDNs under STIC, in this article, time delays in both continuous and discrete system dynamics are well considered. Moreover, the proposed self-triggered mechanism (STM) is an explicit expression, under which the next triggering instant can be derived directly, with simple structure and easy implementation. Finally, two numerical examples are provided to validate the proposed theoretical criteria.