Preserving synchronization under matrix product modifications

Dan Becker-Bessudo, G. Fernandez-Anaya and J.J. Flores-Godoy

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 26, 6631-6645

Abstract: In this article we present a methodology under which stability and synchronization of a dynamical master/slave system configuration are preserved under modification through matrix multiplication. The objective is to show that under a defined multiplicative group, hyperbolic critical points are preserved along the stable and unstable manifolds. The properties of this multiplicative group were determined through the use of simultaneous Jordan decomposition. It is also shown that a consequence of this approach is the preservation of the signature of the Jacobian matrix associated with the dynamical system. To illustrate the results we present several examples of different modified systems.

Keywords: Control; Preservation of synchronization; Chaotic systems; Nonlinear systems; Output feedback and observers (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:26:p:6631-6645

DOI: 10.1016/j.physa.2008.08.016

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