Journal Article

Linear approximations to nonlinear dynamical systems with applications to stability and spectral theory

M. Tomas‐Rodriguez and S. P. Banks

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 20, issue 1, pages 89-103
Published in print March 2003 | ISSN: 0265-0754
Published online March 2003 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/20.1.89
Linear approximations to nonlinear dynamical systems with applications to stability and spectral theory

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In this paper we study a recently introduced technique for nonlinear dynamical systems in which the equation is replaced by a sequence of linear, time‐varying approximations. This allows many of the classical results in linear systems theory to be applied to nonlinear systems. Here we study two particular areas—stability theory and the frequency‐domain theory of nonlinear systems.

Keywords: nonlinear systems; linear approximations; stability; spectral theory

Journal Article.  0 words. 

Subjects: Mathematics

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