Digression on the equivalence between linear 2D discrete repetitive processes and roesser models

摘要

We discuss the equivalence problem between linear 2D discrete repetitive processes and linear 2D discrete Roesser models. Within the constructive algebraic analysis approach to multidimensional (nD) linear systems theory, this equivalence issue is studied by means of isomorphisms of finitely presented modules. In this paper, we prove that every linear 2D discrete repetitive process is equivalent to an explicit linear 2D discrete Roesser model. Comparing this result to [4], [5] where input / output equivalence is concerned, we point out the differences between these two algebraic notions of equivalence while each notion has interesting applications in nD systems theory.