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

Volume

4

fYear

2002

fDate

10-13 Dec. 2002

Firstpage

3918

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;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2002, Proceedings of the 41st IEEE Conference on

ISSN

0191-2216

Print_ISBN

0-7803-7516-5

Type

conf

DOI

10.1109/CDC.2002.1184977

Filename

1184977