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$\cal H_{\infty}$ synchronization of time-delayed chaotic systems. (English) Zbl 1152.93027
Summary: This paper considers $\cal H_{\infty}$ synchronization of a class of time-delayed chaotic systems with external disturbance. Based on Lyapunov theory and Linear Matrix Inequality (LMI) formulation, the dynamic feedback controller is established to not only guarantee synchronization between derive and response systems, but also reduce the effect of external disturbance to an $\cal H_{\infty}$ norm constraint. Then, a criterion for existence of the controller is given in terms of LMIs. Finally, a numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme.

93B52Feedback control
93C73Perturbations in control systems
93D05Lyapunov and other classical stabilities of control systems
93C15Control systems governed by ODE
37D45Strange attractors, chaotic dynamics
Full Text: DOI
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