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IMA Journal of Mathematical Control and Information 1999 16(3):275-297; doi:10.1093/imamci/16.3.275
© 1999 by Institute of Mathematics and its Applications
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Algebraic analysis of linear multidimensional control systems

J. F. POMMARET{dagger} and A. QUADRAT{dagger}

CERMICS, Ecole Nationale des Ponts et Chaussées 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 02, France
{dagger}pommaret{at}ceramics.enpc.fr
{ddagger}quadrat{at}ceramics.enpc.fr

The purpose of this paper is to show how to use the modern methods of algebraic analysis in partial differential 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 duality existing 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,.). All the results are presented through effective algorithms.

Keywords: Control theory; primeness; poles and zeros; multidimensional systems; algebraic analysis; extension functor; janet conjecture; formal theory of partial differential; equations; duality; homological algebra; commutative algebra; noncommutative algebra.


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