Synchronization of hybrid-coupled delayed dynamical networks with noises by partial mixed impulsive control strategy

Abstract

In this paper, a new control method named partial mixed impulsive control strategy is proposed to investigate the problem of exponential synchronization in mean square for a class of general hybrid-coupled delayed dynamical networks with both internal delay and coupling delay. The partial mixed impulsive effects in this strategy can be taken as local and time-varying, which means that they are not only injected into a fraction of nodes in the whole networks but also contain synchronizing and desynchronizing impulses at the same time. In addition, to be more realistic, a delayed coupling term involving the transmission delay and self-feedback delay is taken into account. By means of the Lyapunov method and the comparison principle for impulsive systems, several sufficient criteria are obtained to guarantee the global exponential synchronization in mean square of the dynamical network. The obtained criteria are closely related to the proportion of the controlled nodes, the strengths of mixed impulses, the impulsive intervals, the time delays and the topology structure of the networks. Finally, a numerical example is given to demonstrate the effectiveness of our results.