Global synchronization of nonlinearly coupled Lur’e networks via adaptive feedback control

In this paper, the global synchronization problem of a class of nonlinearly coupled Lur'e networks is focused under adaptive pinning control. Based on the Lyapunov stability theorem, Lipschitz condition and linear matrix inequality, it will be proved that this kind of complex networks can be pinned to a homogenous solution. Furthermore, sufficient conditions for the global synchronization of the nonlinearly coupled complex networks can be derived in view of some linearization methods and S-procedure. Based on the designed adaptive updating laws, some suitable control gains will be obtained. One numerically simulated example of the theoretical results is given.