Synchronization of time-delay dynamical networks via hybrid delayed impulses

This paper investigates the synchronization problem of time-delay dynamical networks by means of hybrid delayed impulses, where synchronizing impulses and desynchronizing impulses can occur simultaneously. Some sufficient synchronization conditions are established based on Razumikhin-type inequality and Lyapunov function. These conditions do not place any limitation on the magnitude of time-delay in dynamical networks. To be specific, it can be less than or greater than the length of impulses intervals and has no magnitude relationship with delays in impulses. Moreover, results indicate that delays in impulses have positive contributions to synchronization. The effectiveness of the theoretical results is demonstrated by two numerical examples.