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A UNIFIED FRAMEWORK FOR SYNCHRONIZATION AND CONTROL OF DYNAMICAL SYSTEMS

Electronics Research Laboratory and Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720, USA

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and

LEON O. CHUA

Electronics Research Laboratory and Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720, USA

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https://doi.org/10.1142/S0218127494000691Cited by:266 (Source: Crossref)

Abstract

In this paper, we give a framework for synchronization of dynamical systems which unifies many results in synchronization and control of dynamical systems, in particular chaotic systems. We define concepts such as asymptotical synchronization, partial synchronization and synchronization error bounds. We show how asymptotical synchronization is related to asymptotical stability. The main tool we use to prove asymptotical stability and synchronization is Lyapunov stability theory. We illustrate how many previous results on synchronization and control of chaotic systems can be derived from this framework. We will also give a characterization of robustness of synchronization and show that master-slave asymptotical synchronization in Chua’s oscillator is robust.