On the conservatism of the sum-of-squares method for analysis of time-delayed systems

Matthew M. Peet, Pierre Alexandre Bliman

Research output: Contribution to journalArticle

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Abstract

In this paper, we present a converse Lyapunov result which shows that using polynomial Lyapunov functionals to prove the stability of linear time-delay systems is not conservative. This result motivates the sum-of-squares approach to stability analysis of linear time-delay systems. This main result is based on an extension of the Weierstrass approximation theorem to show that linear varieties of polynomials can be used to approximate linear varieties of the space of continuous functions.

Original languageEnglish (US)
Pages (from-to)2406-2411
Number of pages6
JournalAutomatica
Volume47
Issue number11
DOIs
StatePublished - Nov 1 2011

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Keywords

  • Function approximation
  • Generated Lyapunov functions
  • Lyapunov stability
  • Polynomials
  • Time delay

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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