Structural stability of equilibrium sets for a class of discontinuous vector fields

Author

Biemond, J. J Benjamin ; Van de Wouw, Nathan ; Nijmeijer, Henk

Author_Institution

Dept. of Mech. Eng., Eindhoven Univ. of Technol., Eindhoven, Netherlands

fYear

2011

fDate

12-15 Dec. 2011

Firstpage

1172

Lastpage

1177

Abstract

A class of discontinuous vector fields is investigated, where equilibria are generically positioned in an interval in the phase space, and equilibria are not isolated points. The dynamics near such an equilibrium set is studied, and it is shown that the structural stability of trajectories near the equilibrium sets is determined by the local dynamics near the endpoints of this interval. Based on this result, sufficient conditions for structural stability of equilibrium sets in planar systems are given, and two new bifurcations are identified. The results are illustrated by application to a controlled mechanical system with dry friction.

Keywords

friction; mechanical engineering; set theory; vectors; controlled mechanical system; discontinuous vector field; dry friction; equilibrium set; phase space; planar system; structural stability; vector field equilibrium; Bifurcation; Eigenvalues and eigenfunctions; Friction; Mechanical systems; Structural engineering; Trajectory; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on

Conference_Location

Orlando, FL

ISSN

0743-1546

Print_ISBN

978-1-61284-800-6

Electronic_ISBN

0743-1546

Type

conf

DOI

10.1109/CDC.2011.6160912

Filename

6160912