An improved augmented delay partitioning approach for the stability of time-varying state-delayed systems

M. N. Alpaslan Parlakci, Ibrahim B. Kucukdemiral

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

Abstract

This paper deals with the asymptotical stability problem of retarded type timedelay systems with time-varying delays using the technique of decomposing the delay interval uniformly into an integer number of equal size segments and proposing an appropriate LyapunovKrasovskii (L-K) functional to develop delay-dependent stability criteria. The novelty of the proposed method originates from two significant contributions. First, a quasi-full size augmented form of L-K functional is introduced for the stability analysis. Second, almost exact full
information has been exploited for the relationship among the actual time-varying delay and its upper bound concerning the delay related integral terms. This approach allows to avoid any redundant enlargement with the delay upper bound while estimating the derivative of the L-K functional as it will bring naturally conservativeness on the results. Several numerical examples are taken into account with some case studies to illustrate the effectiveness of the proposed method. For the treated examples, the results of maximum admissible delay bound have clearly indicated that the proposed approach provides significant improvement over those reported in the literature.
Original languageEnglish
Title of host publication IFAC Proceeding Volumes
PublisherElsevier B.V.
Pages1-6
Number of pages6
Volume45
Edition14
Publication statusPublished - Jun 2012

Publication series

Name IFAC-PapersOnLine
PublisherElsevier
Number14
Volume45
ISSN (Electronic)1474-6670

Fingerprint

Stability criteria
Derivatives

Keywords

  • time-delayed systems
  • delay-partitioning approach
  • time-varying delay
  • stability

Cite this

Parlakci, M. N. A., & Kucukdemiral, I. B. (2012). An improved augmented delay partitioning approach for the stability of time-varying state-delayed systems. In IFAC Proceeding Volumes (14 ed., Vol. 45, pp. 1-6). ( IFAC-PapersOnLine; Vol. 45, No. 14). Elsevier B.V..
Parlakci, M. N. Alpaslan ; Kucukdemiral, Ibrahim B. / An improved augmented delay partitioning approach for the stability of time-varying state-delayed systems. IFAC Proceeding Volumes. Vol. 45 14. ed. Elsevier B.V., 2012. pp. 1-6 ( IFAC-PapersOnLine; 14).
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abstract = "This paper deals with the asymptotical stability problem of retarded type timedelay systems with time-varying delays using the technique of decomposing the delay interval uniformly into an integer number of equal size segments and proposing an appropriate LyapunovKrasovskii (L-K) functional to develop delay-dependent stability criteria. The novelty of the proposed method originates from two significant contributions. First, a quasi-full size augmented form of L-K functional is introduced for the stability analysis. Second, almost exact fullinformation has been exploited for the relationship among the actual time-varying delay and its upper bound concerning the delay related integral terms. This approach allows to avoid any redundant enlargement with the delay upper bound while estimating the derivative of the L-K functional as it will bring naturally conservativeness on the results. Several numerical examples are taken into account with some case studies to illustrate the effectiveness of the proposed method. For the treated examples, the results of maximum admissible delay bound have clearly indicated that the proposed approach provides significant improvement over those reported in the literature.",
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Parlakci, MNA & Kucukdemiral, IB 2012, An improved augmented delay partitioning approach for the stability of time-varying state-delayed systems. in IFAC Proceeding Volumes. 14 edn, vol. 45, IFAC-PapersOnLine, no. 14, vol. 45, Elsevier B.V., pp. 1-6.

An improved augmented delay partitioning approach for the stability of time-varying state-delayed systems. / Parlakci, M. N. Alpaslan; Kucukdemiral, Ibrahim B.

IFAC Proceeding Volumes. Vol. 45 14. ed. Elsevier B.V., 2012. p. 1-6 ( IFAC-PapersOnLine; Vol. 45, No. 14).

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

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N2 - This paper deals with the asymptotical stability problem of retarded type timedelay systems with time-varying delays using the technique of decomposing the delay interval uniformly into an integer number of equal size segments and proposing an appropriate LyapunovKrasovskii (L-K) functional to develop delay-dependent stability criteria. The novelty of the proposed method originates from two significant contributions. First, a quasi-full size augmented form of L-K functional is introduced for the stability analysis. Second, almost exact fullinformation has been exploited for the relationship among the actual time-varying delay and its upper bound concerning the delay related integral terms. This approach allows to avoid any redundant enlargement with the delay upper bound while estimating the derivative of the L-K functional as it will bring naturally conservativeness on the results. Several numerical examples are taken into account with some case studies to illustrate the effectiveness of the proposed method. For the treated examples, the results of maximum admissible delay bound have clearly indicated that the proposed approach provides significant improvement over those reported in the literature.

AB - This paper deals with the asymptotical stability problem of retarded type timedelay systems with time-varying delays using the technique of decomposing the delay interval uniformly into an integer number of equal size segments and proposing an appropriate LyapunovKrasovskii (L-K) functional to develop delay-dependent stability criteria. The novelty of the proposed method originates from two significant contributions. First, a quasi-full size augmented form of L-K functional is introduced for the stability analysis. Second, almost exact fullinformation has been exploited for the relationship among the actual time-varying delay and its upper bound concerning the delay related integral terms. This approach allows to avoid any redundant enlargement with the delay upper bound while estimating the derivative of the L-K functional as it will bring naturally conservativeness on the results. Several numerical examples are taken into account with some case studies to illustrate the effectiveness of the proposed method. For the treated examples, the results of maximum admissible delay bound have clearly indicated that the proposed approach provides significant improvement over those reported in the literature.

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Parlakci MNA, Kucukdemiral IB. An improved augmented delay partitioning approach for the stability of time-varying state-delayed systems. In IFAC Proceeding Volumes. 14 ed. Vol. 45. Elsevier B.V. 2012. p. 1-6. ( IFAC-PapersOnLine; 14).