Study of Singularities in Nonsmooth Dynamical Systems via Singular Perturbation
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Data
2009-01-01
Autores
Llibre, Jaume
da Silva, Paulo R. [UNESP]
Teixeira, Marco A.
Título da Revista
ISSN da Revista
Título de Volume
Editor
Siam Publications
Resumo
In this article we describe some qualitative and geometric aspects of nonsmooth dynamical systems theory around typical singularities. We also establish an interaction between nonsmooth systems and geometric singular perturbation theory. Such systems are represented by discontinuous vector fields on R(l), l >= 2, where their discontinuity set is a codimension one algebraic variety. By means of a regularization process proceeded by a blow-up technique we are able to bring about some results that bridge the space between discontinuous systems and singularly perturbed smooth systems. We also present an analysis of a subclass of discontinuous vector fields that present transient behavior in the 2-dimensional case, and we dedicate a section to providing sufficient conditions in order for our systems to have local asymptotic stability.
Descrição
Palavras-chave
Regularization, Vector fields, Singular perturbation, Discontinuous vector fields, Sliding vector field
Como citar
Siam Journal on Applied Dynamical Systems. Philadelphia: Siam Publications, v. 8, n. 1, p. 508-526, 2009.