Impulsive synchronization of complex-variable network with distributed time delays

Abstract

Impulsive control scheme is adopted to consider the synchronization of complex-variable dynamical network with distributed time delays. Based on the Lyapunov function method and mathematical analysis technique, simple synchronization conditions with respect to system parameters, impulsive gains and intervals are firstly derived. For any given network, the impulsive intervals can be estimated from the derived conditions when the impulsive gains are fixed, and vice versa. Further, adaptive strategy is introduced to design unified impulsive controllers for different networks. Noticeably, in the proposed adaptive impulsive control scheme, the impulsive gains can be adjusted to the needed values and the impulsive instants can be estimated adaptively. Finally, numerical examples are provided to verify the effectiveness of the theoretical results.