Sliding vector fields for non-smooth dynamical systems having intersecting switching manifolds

Nenhuma Miniatura disponível






Curso de graduação

Título da Revista

ISSN da Revista

Título de Volume


Iop Publishing Ltd



Direito de acesso

Acesso restrito


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).




Como citar

Nonlinearity, v. 28, n. 2, p. 493-507, 2015.

Itens relacionados