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Localization and parametrization of linear multidimensional control systems. (English) Zbl 0948.93016
Summary: We study the relation 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 obtained by using Laplace transform, to time-varying ordinary differential control systems and to partial differential control systems with variable coefficients. In particular, we show that the parametrizations obtained by localization are simpler than those obtained by formal duality but are worse in the sense of Palamodov–Kashiwara’s classification of differential modules.

MSC:
93B25 Algebraic methods
93B15 Realizations from input-output data
16D80 Other classes of modules and ideals in associative algebras
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