Globally Exponential Synchronization of Delayed Complex Dynamic Networks With Average Impulsive Delay‐Gain

ABSTRACT In this article, we investigate globally exponential synchronization problems in delayed complex dynamic networks (DCDNs) characterized by both time‐varying impulsive delay and gain (TIDG). Our research is grounded on the Halanay inequality, which serves as the keystone of our analysis. Adopting the method of average impulsive delay‐gain (AIDG), we formulate criteria for globally exponential synchronization dependent on the overall impulsive disturbances. Our criteria reveal the negative effect of AIDG on synchronization, which hinders the synchronization process. Additionally, we refine the concept of average impulsive gain to enhance its applicability. Furthermore, our results demonstrate that even in the simultaneous presence of desynchronizing and synchronizing impulses, along with time‐varying impulsive delays, DCDNs are able to maintain the original synchronization under appropriate conditions, irrespective of whether the average impulsive interval is finite or not. Finally, we validate our theoretical findings by applying them to network examples.