Some simple criteria for pinning a Lur´e network with directed topology

This study considers the pinning synchronisation in a network of coupled Lur´e dynamical systems under directed topology. By using tools from M-matrix theory, S-procedure and Lyapunov functional method, some simple pinning criteria in terms of linear matrix inequalities, whose dimensions are just determined by the size of a single Lur´e node, are derived for Lur´e networks with fixed and designed inner coupling matrices, respectively. A selective pinning scheme is proposed for a directed Lur´e network such that the network can be globally asymptotically pinned to a homogeneous state. Simulation results are provided to illustrate the effectiveness of the theoretical analysis.