Structurally Stable PWL Approximation of Nonlinear Dynamical Systems Admitting Limit Cycles: An Example

Marco BERGAMI  Federico BIZZARRI  Andrea CARLEVARO  Marco STORACE  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.10   pp.2759-2766
Publication Date: 2006/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.10.2759
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: Oscillation, Dynamics and Chaos
Keyword: 
piecewise linear approximation,  nonlinear dynamical systems,  bifurcation analysis,  optimization,  

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Summary: 
In this paper, we propose a variational method to derive the coefficients of piecewise-linear (PWL) models able to accurately approximate nonlinear functions, which are vector fields of autonomous dynamical systems described by continuous-time state-space models dependent on parameters. Such dynamical systems admit limit cycles, and the supercritical Hopf bifurcation normal form is chosen as an example of a system to be approximated. The robustness of the approximations is checked, with a view to circuit implementations.