Asymptotic and structural stability for a linear 2D discrete roesser model

Abstract

Recently we have shown, by providing an explicit counterexample, that the structural stability of a linear 2D discrete Fornasini-Marchesini model is not equivalent to its asymptotic stability when dealing with boundary conditions on the positive axes. The main contribution of the present paper shows that this fact remains valid when dealing with linear 2D discrete Roesser models. Using the notion of equivalence in the sense of the algebraic analysis approach to linear systems theory, we recall that a Fornasini-Marchesini model can always be transformed into an equivalent Roesser model. We then prove that asymptotic stability is preserved by this particular equivalence transformation. We therefore deduce an example of a Roesser model which is asymptotically stable but not structurally stable.