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.

本研究研究了一类具有多个时变时滞的非线性耦合复杂网络的前导跟随问题。引入分布式控制器以实现具有预先已知的不同延迟等级的复杂网络的指数同步。利用Lyapunov稳定性定理和数学归纳法来获得与时滞有关的全局脉冲同步准则。另外，采用了一种自适应策略来建立适合于各种延迟的适当的脉冲间隔。所提出的自适应方案更普遍，更不保守的事实使得能够有效释放由未知延迟量引起的收缩。此外，钉扎脉冲控制方法使得控制成本能够进一步降低。最后，