Stability analysis of linear systems with time-varying delays: Delay uncertainty and quenching

Antonis Papachristodoulou, Matthew M. Peet, Silviu Iulian Niculescu

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

36 Scopus citations

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 46th IEEE Conference on Decision and Control 2007, CDC
Pages2117-2122
Number of pages6
DOIs
StatePublished - Dec 1 2007
Externally publishedYes
Event46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States
Duration: Dec 12 2007Dec 14 2007

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

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

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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    Papachristodoulou, A., Peet, M. M., & Niculescu, S. I. (2007). Stability analysis of linear systems with time-varying delays: Delay uncertainty and quenching. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC (pp. 2117-2122). [4434764] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2007.4434764