Global pinning synchronization of general complex directed networks

In this paper, the global pinning synchronization problem for a class of complex dynamical networks with a target system subject to unknown but bounded control inputs is investigated. One of the major challenges in synchronizing such a complex network is that the control inputs of the target system are totally unknown to any node. Furthermore, the network topology considered here is quite general which does not need to be undirected or satisfy any connectivity conditions. To achieve global pinning synchronization, some non-smooth coupling laws are utilized. By using tools from the Lyapunov stability theory, it is proved that global pinning synchronization in the considered complex network with directed network topology can be ensured if some nodes are appropriately pinned and the control parameters in the present coupling laws are suitably selected.