Accelerating convergence of sum-of-square stability analysis of coupled differential-difference equations

Keqin Gu, Yashun Zhang, Matthew Peet

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

Abstract

This article aims at accelerating the convergence of Lyapunov-Krasovskii stability analysis of coupled differential-difference equations using sum-of-square formulation. Under the assumption that the single integral and double integral terms are both positive definite, a necessary and sufficient condition for the quadratic integral expression is obtained. This result is applied to the Lyapunov-Krasovskii functional and derivative conditions. The method is less conservative than the previous method with identical order of polynomials. The effectiveness of this method is illustrated by numerical examples.

Original languageEnglish (US)
Title of host publicationIFAC Proceedings Volumes (IFAC-PapersOnline)
Pages138-143
Number of pages6
EditionPART 1
StatePublished - 2010
Externally publishedYes
Event9th IFAC Workshop on Time Delay Systems, TDS 2010 - Prague, Czech Republic
Duration: Jun 7 2010Jun 9 2010

Other

Other9th IFAC Workshop on Time Delay Systems, TDS 2010
CountryCzech Republic
CityPrague
Period6/7/106/9/10

Fingerprint

Convergence of numerical methods
Difference equations
Polynomials
Derivatives

Keywords

  • Delay
  • Lyapunov-krasovskii functional
  • Sum-of-square

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Gu, K., Zhang, Y., & Peet, M. (2010). Accelerating convergence of sum-of-square stability analysis of coupled differential-difference equations. In IFAC Proceedings Volumes (IFAC-PapersOnline) (PART 1 ed., pp. 138-143)

Accelerating convergence of sum-of-square stability analysis of coupled differential-difference equations. / Gu, Keqin; Zhang, Yashun; Peet, Matthew.

IFAC Proceedings Volumes (IFAC-PapersOnline). PART 1. ed. 2010. p. 138-143.

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

Gu, K, Zhang, Y & Peet, M 2010, Accelerating convergence of sum-of-square stability analysis of coupled differential-difference equations. in IFAC Proceedings Volumes (IFAC-PapersOnline). PART 1 edn, pp. 138-143, 9th IFAC Workshop on Time Delay Systems, TDS 2010, Prague, Czech Republic, 6/7/10.
Gu K, Zhang Y, Peet M. Accelerating convergence of sum-of-square stability analysis of coupled differential-difference equations. In IFAC Proceedings Volumes (IFAC-PapersOnline). PART 1 ed. 2010. p. 138-143
Gu, Keqin ; Zhang, Yashun ; Peet, Matthew. / Accelerating convergence of sum-of-square stability analysis of coupled differential-difference equations. IFAC Proceedings Volumes (IFAC-PapersOnline). PART 1. ed. 2010. pp. 138-143
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