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

Antonis Papachristodoulou; Matthew M. Peet; Silviu Iulian Niculescu

doi:10.1109/CDC.2007.4434764

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 proceeding › Conference contribution

39 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 language	English (US)
Title of host publication	Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2117-2122
Number of pages	6
ISBN (Print)	1424414989, 9781424414987
DOIs	https://doi.org/10.1109/CDC.2007.4434764
State	Published - 2007
Externally published	Yes
Event	46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: Dec 12 2007 → Dec 14 2007

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	46th IEEE Conference on Decision and Control 2007, CDC
Country/Territory	United States
City	New Orleans, LA
Period	12/12/07 → 12/14/07

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2007.4434764

Cite this

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). Article 4434764 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. 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 M.; Niculescu, Silviu Iulian.
Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc., 2007. p. 2117-2122 4434764 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Papachristodoulou, A, Peet, MM & Niculescu, SI 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., 4434764, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., 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 MM, Niculescu SI. 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. Institute of Electrical and Electronics Engineers Inc. 2007. p. 2117-2122. 4434764. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2007.4434764

Papachristodoulou, Antonis ; Peet, Matthew M. ; Niculescu, Silviu Iulian. / Stability analysis of linear systems with time-varying delays : Delay uncertainty and quenching. Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc., 2007. pp. 2117-2122 (Proceedings of the IEEE Conference on Decision and Control).

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AB - 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.

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

Abstract

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