In this talk, I look at systems of linear PDEs with constant coefficients, and I discuss the relationship between the behaviour defined by the PDEs (ie the solution set), which describes the control system, and certain modules represented by the system equations. The resulting module-behaviour correspondence is surprisingly strong. For example, controllable systems are equivalent to torsionfree modules, and autonomous systems are equivalent to torsion modules. I will look at these and other relationships between the module and behaviour. Furthermore, the algebraic theory allows the application to systems theory problems of standard constructive methods using Groebner bases.
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