Synchronization of Multi-Weighted and Directed Network Under Pinning Impulsive Control

In this paper, multi-weighted and directed complex dynamic networks (MWDCDNs) under the control of hybrid impulses are analyzed. Two cases are considered. In the first case, impulses can be only applied on one fixed node. In the other case, impulses are applied on different nodes according to whether they are synchronized or de-synchronized in MWDCDNs with unbounded time delay. By limiting impulsive interval and Chebyshev distance between the normalized left eigenvectors (NLEVec) of multiple coupling matrices corresponding to the zero eigenvalue, we obtain some criteria for the synchronization of MWDCNs. Some numerical simulation are also given.