Pinning Impulsive Synchronization of Complex Networks with Multiple Sizes of Delays via Adaptive Impulsive Intervals

摘要

The leader-following issue for a class of nonlinearly coupled complex networks with multiple time-varying delays was investigated in this study. A distributed controller was introduced for realizing the exponential synchronization of the complex network with different delay scales that are known in advance. The Lyapunov stability theorem and mathematical induction method were used to obtain delay-dependent criteria for global impulsive synchronization. Additionally, an adaptive strategy was adopted to establish appropriate impulsive intervals suitable for various delays. The fact that the proposed adaptive scheme is more general and less conservative enables the effective release of the constriction caused by unknown delay scales. Furthermore, the pinning impulsive control method enables the control cost to be further reduced. Finally, several numerical simulations were performed to evaluate the effectiveness of the mathematical deductions.