Time scale observability and constructibility of linear dynamic equations. Issue 8 (3rd August 2022)

• Record Type: Journal Article
• Authors: Ben Nasser, Bacem; Djemai, Mohamed; Defoort, Michael; Laleg-Kirati, Taous-Meriem
• Is Part Of: International journal of control. Volume 95:Issue 8(2022)
• Page Start: 1994
• Page End: 2004
• Publication Date: 2022-08-03
• Subjects: Time scales -- dynamic equations -- observability -- constructibility -- reachability -- linear algebra; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2021.1890823
• Languages: English
• ISSNs: 0020-7179

Abstract

Abstract : This paper investigates the observability and constructibility problems of time-varying linear dynamic equations using time scale theory. First, we define observability, reachability and constructibility operators on time scales. Some necessary and sufficient conditions are proposed to ensure the observability on non-uniform time domains based on some linear algebra tools. Then, constructibility is also examined using the same approach. Moreover, the link between observability and constructibility concepts on arbitrary time sets is discussed. Further, the observability and reachability duality relationship for time-varying linear systems on time scales is established. The current work unifies and extends some existing results given for standard cases (i.e. the continuous line and the discrete time domain) to non-uniform time domains. Finally, the obtained results are described with an illustrative example.