Structural Stability and Equivalence of Linear 2D Discrete Systems1

We study stability issues for linear two-dimensional (2D) discrete systems by means of the constructive algebraic analysis approach to linear systems theory. We provide a general definition of structural stability for linear 2D discrete systems which coincides with the existing definitions in the particular cases of the classical Roesser and Fornasini-Marchesini models. We then study the preservation of this structural stability by equivalence transformations. Finally, using the same framework, we consider the stabilization problem for equivalent linear systems.