Distributed synchronization of delayed dynamic networks under asynchronous delay-dependent impulsive control

In this paper, we investigate the distributed synchronization of delayed dynamic networks (DNs) with asynchronous delayed impulsive control. Compared with some related works, the design of delayed impulsive control input allows asynchronous actuation, which is more reasonable for distributed synchronization. The methods of average asynchronous impulsive interval and average asynchronous impulsive delay are used to effectively fetch the delay information existing in asynchronous impulses and integrated to the synchronization of delayed DNs. Some sufficient synchronization criteria for delayed DNs with/without delay are given by using mathematical induction and averaging method. The relationship among impulsive gain, average impulsive interval and average impulsive delays is discussed. The proposed pinning control acts at the asynchronous impulsive instants of the network nodes, which indicates that the time delays existing in asynchronous impulsive control input have a synchronizing effect on the synchronization of delayed DNs. Finally, typical networks are considered to show the validity of asynchronous delayed impulsive control approach.