On the construction of Lyapunov functions using the sum of squares decomposition

A relaxation of Lyapunov's direct method has been proposed elsewhere that allows for an algorithmic construction of Lyapunov functions to prove stability of equilibria in nonlinear systems, but the search is restricted to systems with polynomial vector fields. In the paper, the above technique...

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Bibliographic Details
Published inProceedings of the 41st IEEE Conference on Decision and Control, 2002 Vol. 3; pp. 3482 - 3487 vol.3
Main Authors Papachristodoulou, A., Prajna, S.
Format Conference Proceeding
LanguageEnglish
Published IEEE 2002
Subjects
Biological system modeling
Control systems
Lyapunov method
Nonlinear control systems
Nonlinear systems
Polynomials
Robust stability
Robustness
Sufficient conditions
Uncertainty
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ISBN0780375165
9780780375161
ISSN0191-2216
DOI10.1109/CDC.2002.1184414

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Summary:A relaxation of Lyapunov's direct method has been proposed elsewhere that allows for an algorithmic construction of Lyapunov functions to prove stability of equilibria in nonlinear systems, but the search is restricted to systems with polynomial vector fields. In the paper, the above technique is extended to include systems with equality, inequality, and integral constraints. This allows certain non-polynomial nonlinearities in the vector field to be handled exactly and the constructed Lyapunov functions to contain non-polynomial terms. It also allows robustness analysis to be performed. Some examples are given to illustrate how this is done.
ISBN:0780375165
9780780375161
ISSN:0191-2216
DOI:10.1109/CDC.2002.1184414