Lr-synchronization and adaptive synchronization of a class of chaotic Lurie systems under perturbations

The synchronous control of a class of disturbed chaotic Lurie systems is probed in. The conception of Lr-synchronization of drive-respond systems is presented. Via Lyapunov function analysis and comparison principle, Lr synchronous controller of the drive-respond systems under perturbation is given and its robustness is also discussed. Barbalat lemma is further used to derive the adaptively synchronous controller for the unknown disturbance situation and the globally asymptotical synchronization is realized. All designed controllers are verified by the simulations and the given controllers are linear, which are convenient and can produce rapid convergence speed of the error systems.