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Further results on master-slave synchronization of general Lur’e systems with time-varying delay. (English) Zbl 1146.93031

Summary: A new approach to analyze the asymptotic, exponential and robust stability of the master-slave synchronization for Lur’e systems using time-varying delay feedback control is proposed. The discussion is motivated by the problem of transmitting information in optical communication systems using chaotic lasers. The approach is based on the Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique with the use of a recent Leibniz-Newton model based transformation, without including any additional dynamics. Using the problem of synchronizing coupled Chua’s circuits, three examples are given to illustrate the effectiveness of the proposed methodology.

MSC:

93D09 Robust stability
34D20 Stability of solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93B52 Feedback control
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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