Modules and Behaviours in nD Systems Theory

This paper is intended both as an introduction to the behavioural theory of nD systems, in particular the duality of Oberst and its applications, and also as a bridge between the behavioural theory and the module-theoretic approach of Fliess, Pommaret and others. Our presentation centres on Pommaret's notion of a system observable, and uses this concept to provide new interpretations of known behavioural results. We discuss among other subjects autonomous systems, controllable systems, observability, transfer matrices, computation of trajectories, and system complexity.