A Constructive Algebraic Analysis Approach to the Equivalence of Multidimensional Linear Systems

There exist several models for writing the equations of a multidimensional (nD) linear system and equivalence transformations can be used to pass from one representation to another. Within the constructive algebraic analysis approach to nD linear systems theory, this equivalence issue is studied by means of isomorphisms of finitely presented modules. The present paper illustrates this general algebraic analysis approach by focussing on the equivalence problem for two frequently used 2D models, namely the generalized Fornasini-Marchesini models and the Roesser models.