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IMA Journal of Mathematical Control and Information 2003 20(1):89-103; doi:10.1093/imamci/20.1.89
© 2003 by Institute of Mathematics and its Applications
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Linear approximations to nonlinear dynamical systems with applications to stability and spectral theory

M. Tomas-Rodriguez1 and S. P. Banks1

1 Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK

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.


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