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Nonlinear \(H_\infty\) synchronization of chaotic Lur’e systems. (English) Zbl 0967.93508

Summary: In this paper a master-slave synchronization scheme for Lur’e systems is investigated, which consists of vector field modulation by means of the message signal. Using a full state error feedback mechanism and formulating the synchronization problem within the standard plant framework of modern control theory, it is shown how the original message can be recovered for a class of binary-valued continuous time reference inputs or message signals. Input/output properties of the synchronization scheme are analyzed using the system-theoretical approach of dissipativity with a quadratic storage function and a supply rate of finite \(L_2\)-gain. The feedback matrix is designed such that the influence of the exogenous input on a tracking error is minimized, corresponding to a so-called nonlinear \(H_\infty\) synchronization scheme. Channel noise is taken into account in the design. The method is illustrated on Chua’s circuit and an \(n\)-double scroll circuit.

MSC:

93C10 Nonlinear systems in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93B36 \(H^\infty\)-control
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