Adaptive Synchronization of Complex Dynamical Networks via Distributed Pinning Impulsive Control

摘要

In this paper, exponential synchronization of a class of nonlinearly coupled complex dynamical networks with time-varying delay is investigated. A novel distributed controller combined with pinning impulsive method is designed by selecting the systems with largest norms of errors to be controlled at every impulsive instant. By introducing the adaptive control protocol into the negative feedback controller, suitable control gains are obtained and therefore, the control cost is efficiently saved. Based on the Lyapunov stability theory and some mathematical techniques, some novel leader-following synchronization criteria are derived. Furthermore, with consideration of time-varying impulsive effects, the obtained results are extended to a more complicated situation. Finally, two numerical examples are performed to illustrate the effectiveness of the theoretical analysis.