A necessary and sufficient condition for the stability of interval difference equation via interval Lyapunov equation - Campos, José Renato; Assunção, Edvaldo [UNESP]; Silva, Geraldo Nunes [UNESP]; Lodwick, Weldon Alexander; Leal, Ulcilea Alves Severino (Springer Nature, 2022)
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.
Keywords: Interval difference equation; Interval Lyapunov equation; Interval stability; Interval Sylvester criterion; Single-level constrained interval arithmetic