Further stability criteria for time-delay systems with interval time-varying delays

M.N. Alpaslan Parlakci, I. Beklan Kucukdemiral

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

Abstract

In this paper, a novel stability criterion is developed for time-delay systems having time-varying delays that belong to a given range. Based on a choice of different type of Lyapunov-Krasovskii functional in an extensively augmented form, some new delay-range dependent stability criteria are proposed. This developed stability result has advantages over some previous ones. First, the method is based on the selection of a new, extensively augmented Lyapunov-Krasovskii functional which does not only take the delay range into account but also the weighted version of it. Second it estimates the upper bound of the derivative of the Lyapunov functional without ignoring some useful integral terms. Finally, we have introduced several free slack variables in relation with Newton-Leibniz formula to provide some kind of relaxation for the proposed stability criteria. In addition to this, we have also employed the method of completing to squares which has enabled to provide further relaxation with some additional decision variables.
Original languageEnglish
Title of host publicationProceedings of the 18th World Congress The International Federation of Automatic Control Milano (Italy) August 28 - September 2, 2011
PublisherElsevier B.V.
Pages3867-3872
Number of pages6
DOIs
Publication statusPublished - Jan 2011

Publication series

NameIFAC Proceedings
PublisherElsevier
Number1
Volume44

Fingerprint

Interval Time-varying Delay
Time-delay Systems
Stability Criteria
Lyapunov-Krasovskii Functional
Leibniz' formula
Range of data
Slack variable
Lyapunov Functional
Time-varying Delay
Upper bound
Derivative
Dependent
Term
Estimate

Keywords

  • time-delay
  • interval delays
  • Lyapunov-Krasovskii Functional Stability
  • LMIs

Cite this

Parlakci, M. N. A., & Kucukdemiral, I. B. (2011). Further stability criteria for time-delay systems with interval time-varying delays. In Proceedings of the 18th World Congress The International Federation of Automatic Control Milano (Italy) August 28 - September 2, 2011 (pp. 3867-3872). (IFAC Proceedings; Vol. 44, No. 1). Elsevier B.V.. https://doi.org/10.3182/20110828-6-IT-1002.00111
Parlakci, M.N. Alpaslan ; Kucukdemiral, I. Beklan. / Further stability criteria for time-delay systems with interval time-varying delays. Proceedings of the 18th World Congress The International Federation of Automatic Control Milano (Italy) August 28 - September 2, 2011. Elsevier B.V., 2011. pp. 3867-3872 (IFAC Proceedings; 1).
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Parlakci, MNA & Kucukdemiral, IB 2011, Further stability criteria for time-delay systems with interval time-varying delays. in Proceedings of the 18th World Congress The International Federation of Automatic Control Milano (Italy) August 28 - September 2, 2011. IFAC Proceedings, no. 1, vol. 44, Elsevier B.V., pp. 3867-3872. https://doi.org/10.3182/20110828-6-IT-1002.00111

Further stability criteria for time-delay systems with interval time-varying delays. / Parlakci, M.N. Alpaslan; Kucukdemiral, I. Beklan.

Proceedings of the 18th World Congress The International Federation of Automatic Control Milano (Italy) August 28 - September 2, 2011. Elsevier B.V., 2011. p. 3867-3872 (IFAC Proceedings; Vol. 44, No. 1).

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

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AB - In this paper, a novel stability criterion is developed for time-delay systems having time-varying delays that belong to a given range. Based on a choice of different type of Lyapunov-Krasovskii functional in an extensively augmented form, some new delay-range dependent stability criteria are proposed. This developed stability result has advantages over some previous ones. First, the method is based on the selection of a new, extensively augmented Lyapunov-Krasovskii functional which does not only take the delay range into account but also the weighted version of it. Second it estimates the upper bound of the derivative of the Lyapunov functional without ignoring some useful integral terms. Finally, we have introduced several free slack variables in relation with Newton-Leibniz formula to provide some kind of relaxation for the proposed stability criteria. In addition to this, we have also employed the method of completing to squares which has enabled to provide further relaxation with some additional decision variables.

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Parlakci MNA, Kucukdemiral IB. Further stability criteria for time-delay systems with interval time-varying delays. In Proceedings of the 18th World Congress The International Federation of Automatic Control Milano (Italy) August 28 - September 2, 2011. Elsevier B.V. 2011. p. 3867-3872. (IFAC Proceedings; 1). https://doi.org/10.3182/20110828-6-IT-1002.00111