Notes on strict system equivalence: a generalization of some theorems of Pernebo to multidimensional systems

Strict system equivalence describes the connection between least order realizations of a transfer function in terms of a general linear constant system (Rosenbrock, 1970). It can also be characterized through certain isomorphisms between the solution sets of the system equations (Pernebo, 1977). The paper generalizes this and related results to the case of multidimensional systems, i.e., systems of linear partial difference or differential equations with constant coefficients.