Title :
Condition for bifurcation of the region of attraction in linear planar systems with saturated linear feedback
Author :
Favez, J.-Y. ; Srinivasan, B. ; Mullhaupt, P. ; Bonvin, D.
Author_Institution :
Lab. d´´Autom., Ecole Polytech. Fed. de Lausanne, Switzerland
Abstract :
Bifurcation of the region of attraction for planar systems with one stable and one unstable pole under saturated linear state feedback is considered. The boundary of the region of attraction can either possess an unbounded hyperbolic shape or be a bounded limit cycle. The main contribution of this paper is to provide an analytical condition under which bifurcation occurs. This condition is based on characteristics and position of the stable and unstable manifolds. Furthermore, the exact shape of the region of attraction is provided.
Keywords :
bifurcation; limit cycles; linear systems; poles and zeros; state feedback; analytical condition; bifurcation; bounded limit cycle; hyperbolic shape; linear planar systems; region of attraction; saturated linear feedback; stable manifolds; stable pole; state feedback; unstable manifolds; unstable pole; Bifurcation; Control systems; Limit-cycles; Linear systems; Open loop systems; Shape; State feedback; State-space methods; Symmetric matrices; Vectors;
Conference_Titel :
Decision and Control, 2002, Proceedings of the 41st IEEE Conference on
Print_ISBN :
0-7803-7516-5
DOI :
10.1109/CDC.2002.1184977
