Synchronization of complex dynamical networks via pinning scheme design under hybrid topologies

In this paper, the synchronization problem of complex networks is investigated by pinning control method. A kind of novel hybrid topologies is presented, which includes directed network and undirected network. Under the hybrid topologies, the pinning controllers on the chosen nodes of undirected network are designed to reach synchronization behavior with convex combination of the nodes in direct network. The synchronization criterion is established for reaching pinning control on networks. The results can also extend to networks of networks. The pinning scheme is designed by Cholesky Decomposition and triangularization, which shows that the nodes with low degrees and high degrees should be controlled.