Event-Triggered Impulsive Quasisynchronization of Coupled Dynamical Networks With Proportional Delay.

The quasisynchronization of nonidentically coupled dynamical networks (NCDNs) with proportional delay is achieved by the event-triggered mechanism (ETM). Heterogeneity and proportional delay greatly increase the difficulty on synchronization of NCDNs. As an unbounded delay in the coupling term, proportional delay is dealt with by the comparison principle, constructing parameter equations, and contradiction method. Moreover, different impulsive effects based on ETM are taken into account to reduce the burden of communication, and the quasisynchronization criteria for NCDNs are derived by the impulsive comparison principle and extended variable parameter formula. The synchronization errors and the exponential convergence rates under different impulsive effects are obtained. It is proven that the proposed ETM can avoid Zeno behavior. Finally, examples show the effectiveness of the proposed control scheme.