Stability region analysis using simulations and sum-of-squares programming

Ufuk Topcu, Andrew Packard, Peter Seiler, Timothy Wheeler

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

37 Scopus citations


The problem of computing bounds on the region-of-attraction for systems with polynomial vector fields is considered. Invariant sets of the region-of-attraction are characterized as sublevel sets of Lyapunov functions. Finite dimensional polynomial parameterizations for the Lyapunov functions are used. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of the Lyapunov function candidates are assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute provably invariant subsets of the region-of-attraction and to initialize various bilinear search strategies for further optimization. We illustrate the method on several small examples drawn from the literature.

Original languageEnglish (US)
Title of host publicationProceedings of the 2007 American Control Conference, ACC
Number of pages6
StatePublished - Dec 1 2007
Event2007 American Control Conference, ACC - New York, NY, United States
Duration: Jul 9 2007Jul 13 2007


Other2007 American Control Conference, ACC
Country/TerritoryUnited States
CityNew York, NY


Dive into the research topics of 'Stability region analysis using simulations and sum-of-squares programming'. Together they form a unique fingerprint.

Cite this