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 language | English |
---|---|
Title of host publication | IFAC Proceedings Volumes (IFAC-PapersOnline) |
Publisher | IFAC Secretariat |
Pages | 215-220 |
Number of pages | 6 |
Volume | 48 |
Edition | 12 |
DOIs | |
Publication status | Published - 2015 Jul 1 |
Event | 12th IFAC Workshop on Time Delay Systems, TDS 2015 - Ann Arbor, United States Duration: 2015 Jun 28 → 2015 Jun 30 |
Conference
Conference | 12th IFAC Workshop on Time Delay Systems, TDS 2015 |
---|---|
Country/Territory | United States |
City | Ann Arbor |
Period | 2015/06/28 → 2015/06/30 |
Subject classification (UKÄ)
- Control Engineering
Free keywords
- Discrete-time delay difference equations
- Set invariance
- Time-delay systems