Time scale reachability and controllability of time‐varying linear systems. Issue 5 (21st December 2021)

• Record Type: Journal Article
• Authors: Ben Nasser, Bacem; Djemai, Mohamed; Defoort, Michael; Laleg‐Kirati, Taous‐Meriem
• Is Part Of: Asian journal of control. Volume 24:Issue 5(2022)
• Page Start: 2074
• Page End: 2088
• Publication Date: 2021-12-21
• Subjects: controllability -- linear algebra -- optimal control -- reachability -- time scales -- time‐varying linear systems; Automatic control -- Periodicals; Control theory -- Periodicals; 629.805
• DOI: 10.1002/asjc.2661
• Languages: English
• ISSNs: 1561-8625

Abstract

Abstract: In this paper, we investigate the analysis of reachability and controllability for time‐varying linear systems evolving on nonuniform time domains also known as arbitrary time scales. Based on appropriate operators, some necessary and sufficient conditions are derived to guarantee the reachability for this class of systems using linear algebra tools. Furthermore, a link between optimality and the proposed operators is given. Then, the connection between reachability and controllability analysis on arbitrary time scales is discussed. Through the paper, some examples illustrate the theoretical results.