Reducing the computational cost of the Sum-of-Squares stability test for time-delayed systems

Yashun Zhang, Matthew Peet, Keqin Gu

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

3 Scopus citations

Abstract

This paper considers the problem of reducing the computational complexity associated with the Sum-of-Squares approach to stability analysis of time-delay systems. Specifically, this paper considers systems with a large state-space but with relatively few delays-the most common situation in practice. The paper uses the general framework of coupled differential-difference equations with delays in low-dimensional feedback channels. This framework includes both the standard delayed and neutral-type systems. The approach is based on recent results which introduced a new type of Lyapunov-Krasovskii form which was shown to be necessary and sufficient for stability of this class of systems. This paper shows how exploiting the structure of the new functional can yield dramatic improvements in computational complexity. Numerical examples are given to illustrate this improvement.

Original languageEnglish (US)
Title of host publicationProceedings of the 2010 American Control Conference, ACC 2010
Pages5018-5023
Number of pages6
StatePublished - Oct 15 2010
Externally publishedYes
Event2010 American Control Conference, ACC 2010 - Baltimore, MD, United States
Duration: Jun 30 2010Jul 2 2010

Publication series

NameProceedings of the 2010 American Control Conference, ACC 2010

Other

Other2010 American Control Conference, ACC 2010
CountryUnited States
CityBaltimore, MD
Period6/30/107/2/10

Keywords

  • Complexity
  • Lyapunov-krasovskii
  • Semidefinite programming
  • Sum-of-squares
  • Time delay

ASJC Scopus subject areas

  • Control and Systems Engineering

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  • Cite this

    Zhang, Y., Peet, M., & Gu, K. (2010). Reducing the computational cost of the Sum-of-Squares stability test for time-delayed systems. In Proceedings of the 2010 American Control Conference, ACC 2010 (pp. 5018-5023). [5530749] (Proceedings of the 2010 American Control Conference, ACC 2010).