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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.E89A
No.10
pp.27592766 Publication Date: 2006/10/01
Online ISSN: 17451337
DOI: 10.1093/ietfec/e89a.10.2759
Print ISSN: 09168508 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,
Full Text: PDF(432.6KB)>>
Summary:
In this paper, we propose a variational method to derive the coefficients of piecewiselinear (PWL) models able to accurately approximate nonlinear functions, which are vector fields of autonomous dynamical systems described by continuoustime statespace 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.

