A functorial approach to the behaviour of multidimensional control systems (Q2702503)

The authors apply methods of homological algebra to characterize the obstruction for writing the solution to a linear multidimensional system in implicit form explicitly (cf. the ``behavioural framework''). This is described by the torsion submodule \(t(M)\) of an associated finitely generated module \(M\) (defined by a suitable presentation) over \(A\). \(t(M)\) is seen to be isomorphic to \(\text{ext}^1_A(N, A)\) as well as to \(\text{tor}^A_1(K/ A,M)\). Here, \(N\) is associated to be presentation by duality and \(A\) is a suitable Noetherian integral domain. \(K\) is the quotient field of \(A\). It is also seen that torsion free modules have a weak primeness property.NEWLINENEWLINENEWLINEThis note presents results of the thesis of the second author [Analyse algébrique des systèmes de contrôle linéaires multidimensionels; École des Ponts et Chaussées (1999)].NEWLINENEWLINEFor the entire collection see [Zbl 0952.00062].