Pinning synchronization of complex networks with Lur´e-type nodes and directed switching topology

The global pinning synchronization problem for a class of complex networks with Lur´e-type node dynamics and directed switching network topology has been studied in this paper. The network topology is assumed to switch over a finite set of directed topology candidates under a positive dwell time. The scheme for achieving synchronization engaged in this paper consists of two steps. The first step is to appropriately select some nodes to be pinned such that each possible augmented network topology contains a directed spanning tree rooted at the node describing the target system. The second step is to design the inner linking matrix and the coupling strength of the network to achieve global pinning synchronization. Specifically, two different design algorithms based respectively on M-matrix theory and matrix inequality theory of antistable matrix are provided in the second step. By constructing multiple Lyapunov functions, some sufficient conditions are derived for achieving global pinning synchronization in the considered complex networks.