A converse sum-of-squares Lyapunov result: An existence proof based on the Picard iteration

Matthew Peet, Antonis Papachristodoulou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Citations (Scopus)

Abstract

In this paper, we show that local exponential stability of a polynomial vector field implies the existence of a Lyapunov function which is a sum-of-squares of polynomials. To do that, we use the Picard iteration. This result shows that local stability of polynomial vector fields can be computed in a relatively efficient manner using semidefinite programming.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE Conference on Decision and Control
Pages5949-5954
Number of pages6
DOIs
StatePublished - 2010
Externally publishedYes
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period12/15/1012/17/10

Fingerprint

Picard Iteration
Polynomial Vector Fields
Local Stability
Sum of squares
Converse
Lyapunov
Polynomials
Semidefinite Programming
Exponential Stability
Lyapunov Function
Lyapunov functions
Asymptotic stability
Imply
Polynomial

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Peet, M., & Papachristodoulou, A. (2010). A converse sum-of-squares Lyapunov result: An existence proof based on the Picard iteration. In Proceedings of the IEEE Conference on Decision and Control (pp. 5949-5954). [5717536] https://doi.org/10.1109/CDC.2010.5717536

A converse sum-of-squares Lyapunov result : An existence proof based on the Picard iteration. / Peet, Matthew; Papachristodoulou, Antonis.

Proceedings of the IEEE Conference on Decision and Control. 2010. p. 5949-5954 5717536.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Peet, M & Papachristodoulou, A 2010, A converse sum-of-squares Lyapunov result: An existence proof based on the Picard iteration. in Proceedings of the IEEE Conference on Decision and Control., 5717536, pp. 5949-5954, 2010 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, GA, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5717536
Peet M, Papachristodoulou A. A converse sum-of-squares Lyapunov result: An existence proof based on the Picard iteration. In Proceedings of the IEEE Conference on Decision and Control. 2010. p. 5949-5954. 5717536 https://doi.org/10.1109/CDC.2010.5717536
Peet, Matthew ; Papachristodoulou, Antonis. / A converse sum-of-squares Lyapunov result : An existence proof based on the Picard iteration. Proceedings of the IEEE Conference on Decision and Control. 2010. pp. 5949-5954
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