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

Matthew M. Peet; Antonis Papachristodoulou

doi:10.1109/CDC.2010.5717536

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 proceeding › Conference contribution

14 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 language	English (US)
Title of host publication	2010 49th IEEE Conference on Decision and Control, CDC 2010
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5949-5954
Number of pages	6
ISBN (Print)	9781424477456
DOIs	https://doi.org/10.1109/CDC.2010.5717536
State	Published - 2010
Externally published	Yes
Event	49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, United States Duration: Dec 15 2010 → Dec 17 2010

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	49th IEEE Conference on Decision and Control, CDC 2010
Country/Territory	United States
City	Atlanta
Period	12/15/10 → 12/17/10

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2010.5717536

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). Article 5717536 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. 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 M.; Papachristodoulou, Antonis.
2010 49th IEEE Conference on Decision and Control, CDC 2010. Institute of Electrical and Electronics Engineers Inc., 2010. p. 5949-5954 5717536 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Peet, MM & 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., 5717536, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 5949-5954, 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5717536

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

Abstract

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ASJC Scopus subject areas

Access to Document

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