Piecewise Linear Systems with Closed Sliding Poly-Trajectories

Autor(es)

de Moraes, Jaime R. ^[1] ; da Silva, Paulo R. ^[1]

Afiliação do(s) autor(es)

^[1] UNESP, IBILCE, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN; v. 21, n. 4, p. 653-684, OCT-DEC 2014.
• Citações Web of Science: 0

Resumo

In this paper we study piecewise linear (PWL) vector fields F(x,y) = [ F-+(x,F-y) where x= (x,y) is an element of R-2, F+ (x) = A-Fx b(+) and F- (x) = +, A+ = (at) and A = (a7) are (2 x 2) constant matrices, b+ = (biF,11) E R2 1.1 and b- = (111-, b2-) E IR2 are constant vectors in R2. We suppose that the equilibrium points are saddle or focus in each half-plane. We establish a correspondence between the PWL vector fields and vectors formed by some of the following parameters: sets on E (crossing, sliding or escaping), kind of equilibrium (real or virtual), intersection of manifolds with E, stability and orientation of the focus. Such vectors are called configurations. We reduce the number of configurations by an equivalent relation. Besides, we analyze for which configurations the corresponding PWL vector fields can have or not closed sliding poly-trajectories. (AU)

• Processo FAPESP: 10/17956-1 - Conjuntos Minimais de Sistemas Lineares por Partes
• Beneficiário: Jaime Rezende de Moraes
• Modalidade de apoio: Bolsas no Brasil - Doutorado