Please use this identifier to cite or link to this item:
http://acervodigital.unesp.br/handle/11449/128856
- Title:
- Sliding vector fields for non-smooth dynamical systems having intersecting switching manifolds
- Univ Autonoma Barcelona
- Universidade Estadual Paulista (UNESP)
- Universidade Estadual de Campinas (UNICAMP)
- 0951-7715
- MICIIN/FEDER grant
- Generalitat de Catalunya grant
- ICREA Academia
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
- Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
- Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
- MICIIN/FEDER: MTM2008-03437
- Generalitat de Catalunya: 2009SGR-410
- FP7-PEOPLE-2012-IRSES: 316338
- 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).
- 1-Feb-2015
- Nonlinearity, v. 28, n. 2, p. 493-507, 2015.
- 493-507
- Iop Publishing Ltd
- Non-smooth dynamical system
- Singular perturbation
- Sliding vector field
- http://iopscience.iop.org/article/10.1088/0951-7715/28/2/493/meta;jsessionid=A2FCCC8E3406D079592135B8FAA139C6.c1
- Acesso restrito
- outro
- http://repositorio.unesp.br/handle/11449/128856
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