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Global synchronization of chaotic Lur’e systems via replacing variables control. (English) Zbl 1175.37040
Summary: Finding sufficient criteria for synchronization of master-slave chaotic systems by replacing variables control has been an open problem in the field of chaos control. This paper presents some recent works on the subject, with emphasis on chaos synchronization of both identical and parametrically mismatched Lur’e systems by replacing variables control. The synchronization schemes are formally constructed and two classes of sufficient criteria for global synchronization, linear matrix inequality criterion and frequency-domain criterion, are reviewed and discussed.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
74H65 Chaotic behavior of solutions to dynamical problems in solid mechanics
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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