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On singularly perturbed Filippov systems

Published online by Cambridge University Press:  08 July 2013

PEDRO T. CARDIN ,
PAULO R. DA SILVA  and
MARCO A. TEIXEIRA
PEDRO T. CARDIN
Affiliation:
Departamento de Matemática, Faculdade de Engenharia de Ilha Solteira, UNESP – Univ Estadual Paulista, Rua Rio de Janeiro, 266, CEP 15385-000 Ilha Solteira, São Paulo, Brazil email: pedrocardin@mat.feis.unesp.br
PAULO R. DA SILVA
Affiliation:
Departamento de Matemática, Instituto de Biociências, Letras e Ciências Exatas, UNESP – Univ Estadual Paulista, Rua C. Colombo, 2265, CEP 15054-000 S. J. Rio Preto, São Paulo, Brazil email: prs@ibilce.unesp.br
MARCO A. TEIXEIRA
Affiliation:
IMECC–UNICAMP, CEP 13081-970, Campinas, São Paulo, Brazil email: teixeira@ime.unicamp.br
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Abstract

In this paper, we study singularly perturbed Filippov systems. More specifically, our main question is to know how the dynamics of Filippov systems is affected by singular perturbations. We extend the Fenichel theory developed in Fenichel (J. Differ. Equ., 1979, Vol. 31, pp. 53–98) to these systems. In addition, the study of non-smooth constrained systems is considered.

Keywords

Filippov systemsSliding modeSingular perturbationConstrained systemsImpasse set

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 6 , December 2013 , pp. 835 - 856
Copyright
Copyright © Cambridge University Press 2013 

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