On behavioral equivalence of rational representations

This article deals with the equivalence of representations of behaviors of linear differential systems. In general, the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel representations and image representations. Two kernel representations or image representations are called equivalent if they represent one and the same behavior. For kernel representations defined by polynomial matrices, necessary and sufficient conditions for equivalence are well-known. In this paper, we deal with the equivalence of rational representations, i.e. kernel and image representations that are defined in terms of rational matrices.