Pinning synchronization of switching directed networks with Lorenz-type nodes

This paper is concerned with the global pinning synchronization problem of a class of switching directed networks with Lorenz-type node dynamics. By using tools from M-matrix theory and multiple Lyapunov functions approach, the issues of what kind of nodes should be pinned and how large the control strength of the network should be selected for achieving global synchronization are clearly addressed. It is theoretically shown that the global pinning synchronization can be achieved if the augmented networks always contains a directed spanning tree, the coupling strength is larger than a derived critical value, and the switching among the possible network structures is not too fast.