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Algebraic analysis of linear multidimensional control systems. (English) Zbl 1158.93319
Summary: The purpose of this paper is to show how to use the modern methods of algebraic analysis in control theory, when the input-output relations are defined by systems of partial differential equations in the continuous case or by multi-shift difference equations in the discrete case. The essential tool is the existing duality between the theory of differential modules, or D-modules, and the formal theory of systems of partial differential equations. We reformulate and generalize many formal results that can be found in the extensive literature on multidimensional systems (controllability, primeness concepts, poles and zeros, etc.). All the results are presented through effective algorithms.

MSC:
93B25 Algebraic methods
93C35 Multivariable systems, multidimensional control systems
93C05 Linear systems in control theory
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