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

1 Citation (Scopus)


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.
Number of pages6
Publication statusPublished - Jan 2011
Event18th International Federation of Automatic Control World Congress - Università Cattolica del Sacro Cuore, Milan, Italy
Duration: 28 Aug 20112 Sep 2011

Publication series

NameIFAC Proceedings


Conference18th International Federation of Automatic Control World Congress
Abbreviated title18th IFAC World Congress


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


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