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Set invariance for delay difference equations

Laraba, M. T.; Olaru, S.; Niculescu, S. I.; Bianchini, F.; Giordano, G. LU ; Casagrande, D. and Miani, S. (2015) 12th IFAC Workshop on Time Delay Systems, TDS 2015 In IFAC Proceedings Volumes (IFAC-PapersOnline) 48. p.215-220
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... (More)

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,.

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author
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Discrete-time delay difference equations, Set invariance, Time-delay systems
in
IFAC Proceedings Volumes (IFAC-PapersOnline)
volume
48
pages
6 pages
publisher
IFAC Secretariat
conference name
12th IFAC Workshop on Time Delay Systems, TDS 2015
external identifiers
  • Scopus:84954116590
DOI
10.1016/j.ifacol.2015.09.380
language
English
LU publication?
no
id
d06afc75-c7bd-4874-843b-dc1e33d68085
date added to LUP
2016-07-06 15:19:17
date last changed
2016-10-30 04:48:41
@misc{d06afc75-c7bd-4874-843b-dc1e33d68085,
  abstract     = {<p>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,.</p>},
  author       = {Laraba, M. T. and Olaru, S. and Niculescu, S. I. and Bianchini, F. and Giordano, G. and Casagrande, D. and Miani, S.},
  keyword      = {Discrete-time delay difference equations,Set invariance,Time-delay systems},
  language     = {eng},
  month        = {07},
  pages        = {215--220},
  publisher    = {ARRAY(0xc6d07c8)},
  series       = {IFAC Proceedings Volumes (IFAC-PapersOnline)},
  title        = {Set invariance for delay difference equations},
  url          = {http://dx.doi.org/10.1016/j.ifacol.2015.09.380},
  volume       = {48},
  year         = {2015},
}