Set invariance for delay difference equations

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

Research output: Contribution to journalConference articleScientificpeer-review

5 Citations (Scopus)

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
Pages (from-to)215-220
Number of pages6
JournalIFAC-PapersOnLine
Volume28
Issue number12
DOIs
Publication statusPublished - 1 Jul 2015
Externally publishedYes

Keywords

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

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    Laraba, M. T., Olaru, S., Niculescu, S. I., Blanchini, F., Giordano, G., Casagrande, D., & Miani, S. (2015). Set invariance for delay difference equations. IFAC-PapersOnLine, 28(12), 215-220. https://doi.org/10.1016/j.ifacol.2015.09.380