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Output synchronization of chaotic systems under nonvanishing perturbations. (English) Zbl 1141.93391
Summary: An analysis for chaos synchronization under nonvanishing perturbations is presented. In particular, we use model-matching approach from nonlinear control theory for output synchronization of identical and nonidentical chaotic systems under nonvanishing perturbations in a master-slave configuration. We show that the proposed approach is indeed suitable to synchronize a class of perturbed slaves with a chaotic master system; that is the synchronization error trajectories remain bounded if the perturbations satisfy some conditions. In order to illustrate this robustness synchronization property, we present two cases of study: (i) for identical systems, a pair of coupled Rössler systems, the first like a master and the other like a perturbed slave, and (ii) for nonidentical systems, a Chua’s circuit driving a Rössler/slave system with a perturbed control law, in both cases a quantitative analysis on the perturbation is included.

MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
93C73 Perturbations in control/observation systems
93C10 Nonlinear systems in control theory
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