Stability analysis of linear systems with time-varying delays

Delay uncertainty and quenching

Antonis Papachristodoulou, Matthew Peet, Silviu Iulian Niculescu

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

35 Citations (Scopus)

Abstract

This paper addresses the problem of stability analysis of a class of linear systems with time-varying delays. We develop conditions for robust stability that can be tested using Semidefinite Programming using the Sum of Squares decomposition of multivariate polynomials and the LyapunovKrasovskii theorem. We show how appropriate LyapunovKrasovskii functionals can be constructed algorithmically to prove stability of linear systems with a variation in delay, by using bounds on the size and rate of change of the delay. We also explore the quenching phenomenon, a term used to describe the difference in behaviour between a system with fixed delay and one whose delay varies with time. Numerical examples illustrate changes in the stability window as a function of the bound on the rate of change of delay.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE Conference on Decision and Control
Pages2117-2122
Number of pages6
DOIs
StatePublished - 2007
Externally publishedYes
Event46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States
Duration: Dec 12 2007Dec 14 2007

Other

Other46th IEEE Conference on Decision and Control 2007, CDC
CountryUnited States
CityNew Orleans, LA
Period12/12/0712/14/07

Fingerprint

Linear systems
Quenching
Polynomials
Decomposition
Uncertainty
Robust stability

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Safety, Risk, Reliability and Quality
  • Chemical Health and Safety

Cite this

Papachristodoulou, A., Peet, M., & Niculescu, S. I. (2007). Stability analysis of linear systems with time-varying delays: Delay uncertainty and quenching. In Proceedings of the IEEE Conference on Decision and Control (pp. 2117-2122). [4434764] https://doi.org/10.1109/CDC.2007.4434764

Stability analysis of linear systems with time-varying delays : Delay uncertainty and quenching. / Papachristodoulou, Antonis; Peet, Matthew; Niculescu, Silviu Iulian.

Proceedings of the IEEE Conference on Decision and Control. 2007. p. 2117-2122 4434764.

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

Papachristodoulou, A, Peet, M & Niculescu, SI 2007, Stability analysis of linear systems with time-varying delays: Delay uncertainty and quenching. in Proceedings of the IEEE Conference on Decision and Control., 4434764, pp. 2117-2122, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434764
Papachristodoulou A, Peet M, Niculescu SI. Stability analysis of linear systems with time-varying delays: Delay uncertainty and quenching. In Proceedings of the IEEE Conference on Decision and Control. 2007. p. 2117-2122. 4434764 https://doi.org/10.1109/CDC.2007.4434764
Papachristodoulou, Antonis ; Peet, Matthew ; Niculescu, Silviu Iulian. / Stability analysis of linear systems with time-varying delays : Delay uncertainty and quenching. Proceedings of the IEEE Conference on Decision and Control. 2007. pp. 2117-2122
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