An improved stability method for linear systems with fast-varying delays

Eugenii Shustin*, Emilia Fridman

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Stability of linear systems with uncertain bounded time-varying delays is studied under the assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound of the L2-norm of a certain integral operator. There exists a bound on this operator in two cases: in the case where the delay derivative is not greater than 1 and in the case without any constraints on the delay derivative. In the present note we fill the gap between the two cases by deriving a tight operator bound which is an increasing and continuous function of the delay derivative upper bound d >1. For d → 1 the new bound corresponds to the second case and improves the existing bound. As a result, delay-derivative-dependent frequency-domain and time-domain stability criteria are derived for systems with the delay derivative greater than 1.

Original languageEnglish
Title of host publicationROCOND'06 - 5th IFAC Symposium on Robust Control Design, Final Program with Abstracts
PublisherIFAC Secretariat
Number of pages6
EditionPART 1
ISBN (Print)9783902661104
StatePublished - 2006

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
NumberPART 1
ISSN (Print)1474-6670


  • Input-output approach
  • Stability
  • Time-varying delay


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