On the positivity and asymptotic stability of the fractional 2D hybrid linear Roesser model

Abstract

The aim of this paper is to introduce a new 2D fractional hybrid linear system described by the Roesser model with the conformable fractional derivative in the continuous time variables and the fractional difference in the discrete part. The solution of the considered model is derived. The positivity conditions are then extracted and the Cayley–Hamilton theorem is extended. A new necessary and sufficient conditions for the asymptotic stability of the proposed positive fractional 2D hybrid linear model are then established. Finally, some numerical examples are presented to show the applicability and the effectiveness of the presented methods.