Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/244362
Type: Artigo de periódico
Title: Sliding Vector Fields For Non-smooth Dynamical Systems Having Intersecting Switching Manifolds
Author: Llibre
Jaume; da Silva
Paulo R.; Teixeira
Marco A.
Abstract: We consider a differential equation p over dot = X(p), p is an element of R-3, with discontinuous right-hand side and discontinuities occurring on a set Sigma. We discuss the dynamics of the sliding mode which occurs when, for any initial condition near p is an element of Sigma, the corresponding solution trajectories are attracted to Sigma. Firstly we suppose that Sigma = H-1(0), where H is a smooth function and 0 is an element of R is a regular value. In this case Sigma is locally diffeomorphic to the set F = {(x, y, z) is an element of R-3; z = 0}. Secondly we suppose that Sigma is the inverse image of a non-regular value. We focus our attention to the equations defined around singularities as described in Gutierrez and Sotomayor (1982 Proc. Lond. Math. Soc 45 97-112). More precisely, we restrict the degeneracy of the singularity so as to admit only those which appear when the regularity conditions in the definition of smooth surfaces of R-3 in terms of implicit functions and immersions are broken in a stable manner. In this case Sigma is locally diffeomorphic to one of the following algebraic varieties: D = {(x, y, z) is an element of R-3; xy = 0} (double crossing); T = {(x, y, z) is an element of R-3; xyz = 0} (triple crossing); C = {(x, y, z) is an element of R-3; z(2) -x(2)-y(2) = 0} (cone) or W = {(x, y, z) is an element of R-3; zx(2)-y(2) = 0} (Whitney's umbrella).
Subject: Singular Perturbation
Country: BRISTOL
Editor: IOP PUBLISHING LTD
Rights: fechado
Identifier DOI: 10.1088/0951-7715/28/2/493
Address: http://iopscience.iop.org/article/10.1088/0951-7715/28/2/493/meta;jsessionid=A2FCCC8E3406D079592135B8FAA139C6.c1
Date Issue: 2015
Appears in Collections:Unicamp - Artigos e Outros Documentos

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