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

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

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 part...

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Veröffentlicht in:IMA journal of mathematical control and information 2003-03, Vol.20 (1), p.89-103
Hauptverfasser: Tomas‐Rodriguez, M., Banks, S. P.
Format: Artikel
Sprache:eng
Schlagworte:
linear approximations
nonlinear systems
spectral theory
stability
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Zusammenfassung: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.
ISSN:0265-0754
1471-6887
DOI:10.1093/imamci/20.1.89