\(\mu \)-Synchronization of Complex Networks with Unbounded Delay Under Hybrid Impulsive Control

摘要

For impulsive system, there are two types of impulses, stabilizing impulses and destabilizing impulses. Most papers considered them separately, while in this paper, our general model will contain them simultaneously, i.e., these two impulses exist hybridly. Moreover, the time delay is also allowed to be unbounded, which is another main difference with previous papers. At first, a new \(\mu \)-stability is defined, then based on impulsive control theory, a criterion of \(\mu \)-stability for impulsively controlled system is set up. Compared with exponential stability under hybrid impulses and unbounded delays, the conditions for \(\mu \)-stability are less conservative. Secondly, we apply it on complex dynamic networks with hybrid impulses and unbounded time delays, and corresponding criteria for \(\mu \)-synchronization are also obtained. Finally, numerical examples are presented to illustrate the feasibility of theoretical results.