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We discuss implicit systems of ordinary linear differential equations with (time-) variable coefficients, their solutions in the signal space of hyperfunctions according to Sato and their solution spaces, called time-varying linear systems or behaviours, from the system theoretic point of view. The basic result, inspired by an analogous one for multidimensional constant linear systems, is a duality...
We study the link existing between the parametrization of differential operators by potential-like arbitrary functions and the localization of differential modules, while applying these results to the parametrization of linear multidimensional control systems. We show that the localization of differential modules is a natural way to generalize some well-known results on transfer matrix, classically...
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