Rigorous Verification of Poincare Map Generated by a Continuous Piece-Wise Linear Vector Field and Its Application

Hideaki OKAZAKI
Katsuhide FUJITA
Hirohiko HONDA
Hideo NAKANO

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E88-A    No.4    pp.810-817
Publication Date: 2005/04/01
Online ISSN: 
DOI: 10.1093/ietfec/e88-a.4.810
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Selected Papers from the 17th Workshop on Circuits and Systems in Karuizawa)
Category: 
Keyword: 
interval arithmetic,  computer assisted rigorous proof,  Poincare map,  canard,  slow-fast system,  continuous piece-wise linear vector field,  

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Summary: 
This paper provides algorithms in order to solve an interval implicit function of the Poincare map generated by a continuous piece-wise linear (CPWL) vector field, with the use of interval arithmetic. The algorithms are implemented with the use of MATLAB and INTLAB. We present an application to verification of canards in two-dimensional CPWL vector field appearing in nonlinear piecewise linear circuits frequently, and confirm that the algorithms are effective.

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