Stafford's reduction of linear partial differential systems
Proceedings of SSSC 2013, Grenoble (France)
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Abstract:
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 Stafford. The purpose of this paper is to make some results
obtained in Stafford 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).