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${L}_{r}$-synchronization and adaptive synchronization of a class of chaotic Lurie systems under perturbations. (${L}_{r}$-synchronization and adaptive synchronization of a class of chaotic Lur’e systems under perturbations.) (English) Zbl 1239.93050
Summary: The synchronous control of a class of disturbed chaotic Lur’e systems is probed in. The conception of ${L}_{r}$-synchronization of drive-respond systems is presented. Via Lyapunov function analysis and comparison principle, a ${L}_{r}$ synchronous controller of the drive-respond systems under perturbation is given and its robustness is also discussed. Barbalat’s lemma is further used to derive the adaptively synchronous controller for the unknown disturbance situation and the globally asymptotic 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.
##### MSC:
 93C15 Control systems governed by ODE 34H10 Chaos control (ODE) 93C73 Perturbations in control systems