Enhancement of the Quality and Robustness in Synchronization of Nonlinear Lur'e Dynamical Networks

In order to improve the synchronous reliability and dependability of complex dynamical networks, methods need to be proposed to enhance the quality and robustness of the synchronization scheme. The present study focuses on the robust fault detection issue within the synchronization for a class of nonlinear dynamical networks composed by identical Lur'e systems. Sufficient conditions in terms of linear matrix inequalities (LMIs) are established to guarantee global robust synchronization of the network. Under such a synchronization scheme, the error dynamical system is globally asymptotically stable, the effect of external disturbances is suppressed, and at the same time, the network is sensitive to possible faults based on a mixed performance. The fault sensitivity index, moreover, can be optimized via a convex optimization algorithm. The effectiveness and applicability of the analytical results are demonstrated through a network example composed by the Chua's circuit, and it shows that the quality and robustness of synchronization has been greatly enhanced.