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Zbl 1239.93050
He, Hanlin; Tu, Jianjun; Xiong, Ping
$L_{r}$-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)
[J] J. Franklin Inst. 348, No. 9, 2257-2269 (2011). ISSN 0016-0032; ISSN 1879-2693/e

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 2000:: *93C15 Control systems governed by ODE
34H10
93C73 Perturbations in control systems

Keywords: synchronous control; class of disturbed chaotic Lur'e systems; Lyapunov function; Barbalat's lemma; globally asymptotic synchronization

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