Kalman type rank condition for relative controllability of second order delayed linear difference equations
Journal of Difference Equations and Applications, vol.31, no.11, pp.1439-1456, 2025 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 31 Issue: 11
- Publication Date: 2025
- Doi Number: 10.1080/10236198.2025.2560013
- Journal Name: Journal of Difference Equations and Applications
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
- Page Numbers: pp.1439-1456
- Keywords: delayed linear discrete systems, Kalman type rank condition, Relative controllability, second-order difference
- Open Archive Collection: Article
- Azerbaijan State University of Economics (UNEC) Affiliated: Yes
Abstract
This paper explores the relative controllability of second-order delayed linear difference systems. Initially, we establish a Kalman-type rank condition as a fundamental criterion for assessing controllability. Following this, we introduce the discrete Gramian matrix and demonstrate its nonsingularity, supported by several auxiliary lemmas. Additionally, we derive a sufficient condition for relative controllability and construct an appropriate control function. To validate the theoretical results, a numerical example is presented that illustrates the practical implications and effectiveness of the proposed approach.