Synchronization control of hybrid-coupled heterogeneous complex networks

This paper is concerned with the problem of synchronization control for the delayed hybrid-coupled heterogeneous network with stochastic disturbances. To begin with, the open-loop control is imposed on the whole network, based on which the pinning adaptive control and the impulsive control are introduced to synchronize the whole network to an arbitrary objective trajectory. Furthermore, by employing stochastic analysis techniques and the improved Halanay inequality, some easy-to-verify sufficient conditions are derived to guarantee the asymptotic/exponential synchronization in the mean square of the complex network under study. Numerical example of a directed network is illustrated to demonstrate the applicability and efficiency of the proposed theoretical results.