Abstract
Interval difference equations can be used for modeling biological, economic, or physical systems that, due to lack of information or measurement errors in the input data from real-world applications, contain uncertainties. These types of systems are usually called uncertain systems. The stability analysis of those systems is of particular interest among the various properties of the uncertain systems. In this paper, we propose a necessary and sufficient condition for the stability of linear interval difference equation using single-level constrained interval arithmetic. The interval Lyapunov matrix equation is developed coupled with the interval Sylvester criterion. The stability analysis of the interval difference equation proposed here, using constrained interval arithmetic, is, to a certain degree, similar to the case in crisp environment. This similarity is of great advantage for the treatment of systems with uncertainty. We illustrate the application of the stability theory developed here with a variety of examples.
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Acknowledgements
The authors are very much thankful to the anonymous reviewers for their constructive comments. The first author is grateful to Federal Institute of Education, Science and Technology of São Paulo.
Funding
Edvaldo Assunção was partially supported by the Brazilian National Council for Scientific and Technological Development (CNPq) under Grant Number 301227/2017-9. Geraldo Nunes Silva was partially supported by the São Paulo State Research Foundation (FAPESP – CEPID) under Grant Number 2013/07375-0 and 18/08036-8. Weldon Alexander Lodwick was also partially supported by CNPq [Grant Number 400754/2014-2].
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Campos, J.R., Assunção, E., Silva, G.N. et al. A necessary and sufficient condition for the stability of interval difference equation via interval Lyapunov equation. Soft Comput 26, 5043–5056 (2022). https://doi.org/10.1007/s00500-022-06958-4
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DOI: https://doi.org/10.1007/s00500-022-06958-4