Dissipative lag synchronization of chaotic Lur'e systems with unknown disturbances

This paper is concerned with the problem of dissipative lag synchronization (LS) for two identical Lur'e systems with unknown external disturbances. The disturbances are supposed to be generated by the exogenous systems with and without time-delay. Based on the disturbance-observer-based control method, the linear matrix inequality technique and the dissipativity theory, the disturbance observers are developed to ensure the boundedness of the disturbance error dynamics and the dissipativity of the resultant LS error system. By using the sliding-mode control (SMC) approach, an integral-type sliding surface function is constructed and a dissipative SMC law is established to render the disturbance rejection and realize LS between the master and slave systems, and an integral sliding-mode controller is designed to guarantee the reachability of the specified sliding surface. Finally, the Chua's circuit is used as a numerical example to illustrate the effectiveness of the proposed method.