Set invariance for delay difference equations
(2015) 12th IFAC Workshop on Time Delay Systems, TDS 2015 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
- Laraba, M. T. ; Olaru, S. ; Niculescu, S. I. ; Bianchini, F. ; Giordano, G. LU ; Casagrande, D. and Miani, S.
- organization
- publishing date
- 2015-07-01
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Discrete-time delay difference equations, Set invariance, Time-delay systems
- host publication
- IFAC Proceedings Volumes (IFAC-PapersOnline)
- volume
- 48
- edition
- 12
- pages
- 6 pages
- publisher
- IFAC Secretariat
- conference name
- 12th IFAC Workshop on Time Delay Systems, TDS 2015
- conference location
- Ann Arbor, United States
- conference dates
- 2015-06-28 - 2015-06-30
- 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
- 2022-04-11 12:25:15
@inproceedings{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.}}, booktitle = {{IFAC Proceedings Volumes (IFAC-PapersOnline)}}, keywords = {{Discrete-time delay difference equations; Set invariance; Time-delay systems}}, language = {{eng}}, month = {{07}}, pages = {{215--220}}, publisher = {{IFAC Secretariat}}, title = {{Set invariance for delay difference equations}}, url = {{http://dx.doi.org/10.1016/j.ifacol.2015.09.380}}, doi = {{10.1016/j.ifacol.2015.09.380}}, volume = {{48}}, year = {{2015}}, }