A behavioural/algebraic approach to multidimensional systems theory

The field of multidimensional systems theory suffers from the lack of a framework in which its many diverse strands could be unified. We propose the behavioural approach as such a framework. In the study of autoregressive systems, the use of behavioural tools is particularly useful since it allows the application of Oberst´s duality theory, in which every AR nD behaviour is identified with a unique finitely generated module over the polynomial (Laurent polynomial) ring in n indeterminates. We have illustrated the efficacy of this approach by considering a fundamental algebraic concept, the annihilator of a module. We have shown that this concept relates to the autonomy of a behaviour, the idea of poles of an nD system, and notions of primeness and Bezout identities. We believe that the combination of the behavioural approach with algebraic techniques is suitable for the unification and solution of many problems in the study of multidimensional linear shift invariant systems