A unified synchronization criterion for impulsive dynamical networks

This paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks. Two types of impulses are considered: synchronizing impulses and desynchronizing impulses. In previous literature, all of the results are devoted to investigating these two kinds of impulses separately. Thus a natural question arises: Is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses? In this paper, a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named “average impulsive interval”. The derived criterion is theoretically and numerically proved to be less conservative than existing results. Numerical examples including scale-free and small-world structures are given to show that our results are applicable to large-scale networks.