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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
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2006/10/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: Oscillation, Dynamics and Chaos
piecewise linear approximation, nonlinear dynamical systems, bifurcation analysis, optimization,
Full Text: PDF(432.6KB)>>
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.