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

Matthew M. Peet, Antonis Papachristodoulou

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

12 Scopus citations

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 publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages5949-5954
Number of pages6
DOIs
StatePublished - Dec 1 2010
Externally publishedYes
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

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

ASJC Scopus subject areas

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

Fingerprint Dive into the research topics of 'A converse sum-of-squares Lyapunov result: An existence proof based on the Picard iteration'. Together they form a unique fingerprint.

  • Cite this

    Peet, M. M., & Papachristodoulou, A. (2010). A converse sum-of-squares Lyapunov result: An existence proof based on the Picard iteration. In 2010 49th IEEE Conference on Decision and Control, CDC 2010 (pp. 5949-5954). [5717536] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2010.5717536