Positive forms and stability of linear time-delay systems

Matthew Peet, Antonis Papachristodoulou, Sanjay Lall

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

25 Scopus citations

Abstract

We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that stability implies that there exists a quadratic Lyapunov function on the state space, although this is in general infinite dimensional. We give an explicit parametrization of a finite-dimensional subset of the cone of Lyapunov functions. Positivity of this class of functions is enforced using sum-of-squares polynomial matrices. This allows the computation to be formulated as a semidefinite program.

Original languageEnglish (US)
Title of host publicationProceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages187-193
Number of pages7
ISBN (Print)1424401712, 9781424401710
DOIs
StatePublished - 2006
Externally publishedYes
Event45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States
Duration: Dec 13 2006Dec 15 2006

Publication series

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

Other

Other45th IEEE Conference on Decision and Control 2006, CDC
Country/TerritoryUnited States
CitySan Diego, CA
Period12/13/0612/15/06

ASJC Scopus subject areas

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

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