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.
|Original language||English (US)|
|Number of pages||11|
|Journal||International Journal of Control|
|State||Published - Mar 25 2021|
Bibliographical noteKAUST Repository Item: Exported on 2021-03-29
Acknowledged KAUST grant number(s): BAS/1/1627-01-01
Acknowledgements: Research reported in this publication was supported by King Abdullah University of Science and Technology (KAUST) through the base research fund under grant number BAS/1/1627-01-01.
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications