Analysis of polynomial systems with time delays via the sum of squares decomposition

Antonis Papachristodoulou, Mathew M. Peet, Sanjay Lall

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


We present a methodology for analyzing robust independent-of-delay and delay-dependent stability of equilibria of systems described by nonlinear Delay Differential Equations by algorithmically constructing appropriate Lyapunov-Krasovskii functionals using the sum of squares decomposition of multivariate polynomials and semidefinite programming. We illustrate the methodology using an example from population dynamics.

Original languageEnglish (US)
Pages (from-to)1058-1064
Number of pages7
JournalIEEE Transactions on Automatic Control
Issue number5
StatePublished - 2009
Externally publishedYes


  • Linear matrix inequality (LMI)
  • Lyapunov-Krasovskii
  • Sum of squares (SOS)
  • Time delay

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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