Stafford's Reduction of Linear Partial Differential Systems

It is well-known that linear systems theory can been studied by means of module theory. In particular, to a linear ordinary/partial differential system corresponds a finitely presented left module over a ring of ordinary/partial differential operators. The structure of modules over rings of partial differential operators was investigated in Stafford's seminal work [18]. The purpose of this paper is to make some results obtained in [18] constructive. Our results are implemented in the Maple package Stafford. Finally, we give system-theoretic interpretations of Stafford's results within the behavioural approach (e.g., minimal representations, autonomous behaviours, direct decomposition of behaviours, differential flatness).