Set Invariance for Delay Difference Equations

M.T. Laraba 1, 2 Sorin Olaru 3, 1, 2 Silviu-Iulian Niculescu 2, 3 F. Blanchini 2 G. Giordano 4 D. Casagrande 2 S. Miani 4
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : This paper deals with set invariance for time delay systems. The first goal of the paper is to review the known necessary or su?cient 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 su?cient condition for the existence of ellipsoidal D-contractive sets for dDDEs, and a necessary and su?cient condition for the existence of Dinvariant sets in relation to time-varying dDDE stability. Another contribution is the clarification of the relationship between convexity (convex hull operation) and D-invariance.Inshort, tis 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.
Keywords : Set invariance
Document type :
Conference papers
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https://hal-centralesupelec.archives-ouvertes.fr/hal-01260095
Contributor : Pascale Lepeltier <>
Submitted on : Thursday, January 21, 2016 - 3:01:23 PM
Last modification on : Tuesday, June 25, 2019 - 1:26:24 AM

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M.T. Laraba, Sorin Olaru, Silviu-Iulian Niculescu, F. Blanchini, G. Giordano, et al.. Set Invariance for Delay Difference Equations. 12th IFAC Workshop on Time Delay Systems TDS 2015, Jun 2015, ANN ARBOR- Michigan, United States. ⟨10.1016/j.ifacol.2015.09.380⟩. ⟨hal-01260095⟩

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