Stafford's reduction of linear partial differential systems
Résumé
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. The purpose of this paper is to make some of Stafford's results 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).