DocumentCode
2080223
Title
A Lyapunov function proof of Poincare´s theorem
Author
Haddad, Wassim M. ; Nersesov, Sergey G. ; Chellaboina, VijaySekhar
Author_Institution
Sch. of Aerosp. Eng., Georgia Inst. of Technol., Atlanta, GA, USA
Volume
5
fYear
2002
fDate
2002
Firstpage
3922
Abstract
One of the most fundamental results in analyzing the stability properties of periodic orbits and limit cycles of dynamical systems is Poincare´s theorem. The proof of this result involves system analytic arguments along with the Hartman-Grobman theorem. In this paper, using the notions of stability of sets, we construct lower semicontinuous Lyapunov functions to provide a Lyapunov function proof of Poincare´s theorem.
Keywords
Lyapunov methods; control system analysis; stability; Lyapunov function; Poincare´s theorem; dynamical systems; limit cycles; periodic orbits; stability properties; Aerospace engineering; Limit-cycles; Lyapunov method; Mechanical factors; Orbits; Stability analysis; Sufficient conditions; Trajectory;
fLanguage
English
Publisher
ieee
Conference_Titel
American Control Conference, 2002. Proceedings of the 2002
ISSN
0743-1619
Print_ISBN
0-7803-7298-0
Type
conf
DOI
10.1109/ACC.2002.1024541
Filename
1024541
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