DocumentCode :
2818651
Title :
A theorem of the alternative for SOS Lyapunov functions
Author :
Peyrl, Helfried ; Parrilo, Pablo A.
Author_Institution :
ETH Zurich, Zurich
fYear :
2007
fDate :
12-14 Dec. 2007
Firstpage :
1687
Lastpage :
1692
Abstract :
In this paper duality theory is used to derive a theorem of the alternative for the existence of a sums of squares (SOS) Lyapunov function for a nonlinear system described by a polynomial vector field. We show that moments of occupation measures of unstable trajectories are dual feasible solutions providing a natural interpretation of the elements in the dual space. We show that moments corresponding to equilibria, orbits, and unbounded solutions indeed provide a certificate of infeasibility of the SOS Lyapunov problem. Additionally, equilibrium points may be recovered from special dual solutions.
Keywords :
Lyapunov methods; duality (mathematics); nonlinear control systems; polynomials; vectors; dual space; duality theory; nonlinear system; occupation measures; polynomial vector field; sums of squares Lyapunov functions; Control systems; Extraterrestrial measurements; Functional analysis; Linear systems; Lyapunov method; Nonlinear systems; Orbits; Polynomials; Stability; Time measurement;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control, 2007 46th IEEE Conference on
Conference_Location :
New Orleans, LA
ISSN :
0191-2216
Print_ISBN :
978-1-4244-1497-0
Electronic_ISBN :
0191-2216
Type :
conf
DOI :
10.1109/CDC.2007.4434258
Filename :
4434258
Link To Document :
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