Title :
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
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;
Conference_Titel :
Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
978-1-61284-800-6
Electronic_ISBN :
0743-1546
DOI :
10.1109/CDC.2011.6160912
