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.

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