Set invariance for delay difference equations

M. T. Laraba, S. Olaru, S. I. Niculescu, F. Bianchini, G. Giordano, D. Casagrande, S. Miani

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review

Abstract

This paper deals with set invariance for time delay systems. The first goal of the paper is to review the known necessary or sufficient conditions for the existence of invariant sets with respect to dynamical systems described by discrete-time delay difference equations (dDDEs). Secondly, we address the construction of invariant sets in the original state space (also called D-invariant sets) by exploiting the forward mappings. As novelties, the present paper contains a sufficient condition for the existence of ellipsoidal D-contractive sets for dDDEs, and a necessary and sufficient condition for the existence of 22-invariant sets in relation to time-varying dDDE stability. Another contribution is the clarification of the relationship between convexity (convex hull operation) and D-invariance. In short, it is shown that the convex hull of two D-invariant sets is not D-invariant but the convex hull of a non-convex D-invariant, set is D-invariant,.

Original languageEnglish
Title of host publicationIFAC Proceedings Volumes (IFAC-PapersOnline)
PublisherIFAC Secretariat
Pages215-220
Number of pages6
Volume48
Edition12
DOIs
Publication statusPublished - 2015 Jul 1
Event12th IFAC Workshop on Time Delay Systems, TDS 2015 - Ann Arbor, United States
Duration: 2015 Jun 282015 Jun 30

Conference

Conference12th IFAC Workshop on Time Delay Systems, TDS 2015
Country/TerritoryUnited States
CityAnn Arbor
Period2015/06/282015/06/30

Subject classification (UKÄ)

  • Control Engineering

Free keywords

  • Discrete-time delay difference equations
  • Set invariance
  • Time-delay systems

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