An LMI approach to stability of discrete delay systems

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During the last decade, a considerable amount of attention has been payed to stability and control of continuous-time linear systems with delays (see e.g. [?], [?], [?], [?]-[?] and the references therein). Delay-independent and, less conservative, delay-dependent sufficient stability conditions in terms of Riccati or linear matrix inequalities (LMIs) have been derived by using Lyapunov-Krasovskii functionals or Lyapunov-Razumikhin functions. Delay-dependent conditions are based on different model transformations. The most recent one, a descriptor representation of the system [?]-[?], minimizes the overdesign that stems from the model transformation used. The conservatism that stems from the bounding of the cross-terms in the derivation of the derivative of the Lyapunov-Krasovskii functional has also been significantly reduced in the past few years. An important result that improves the standard bounding technique of e.g. [?] has been proposed in [?].

Original languageEnglish
Title of host publicationEuropean Control Conference, ECC 2003
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9783952417379
StatePublished - 13 Apr 2003
Event2003 European Control Conference, ECC 2003 - Cambridge, United Kingdom
Duration: 1 Sep 20034 Sep 2003

Publication series

NameEuropean Control Conference, ECC 2003


Conference2003 European Control Conference, ECC 2003
Country/TerritoryUnited Kingdom


  • Delay-dependent conditions
  • Discrete systems
  • Lyapunov functionals
  • Norm-bounded uncertainties
  • Time-delay systems


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