Fröhler, Stefan; Oberst, Ulrich Continuous time-varying linear systems. (English) Zbl 0909.93041 Syst. Control Lett. 35, No. 2, 97-110 (1998). Summary: 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 theorem which establishes a categorical one–one correspondence between time-varying linear systems or behaviours and finitely generated modules over a suitable skew-polynomial ring of differential operators. This theorem is false for the signal spaces of infinitely often differentiable functions or of meromorphic (hyper-) functions or of distributions on \({\mathbb{R}} \). It is used to obtain various results on key notions of linear system theory. Several new algorithms for modules over rings of differential operators and, in particular, new Gröbner basis algorithms due to Insa and Pauer make the system theoretic results effective. Cited in 12 Documents MSC: 93C99 Model systems in control theory 93B25 Algebraic methods 93A99 General systems theory 93B15 Realizations from input-output data 93C05 Linear systems in control theory Keywords:nonautonomous system; controllability; differential operator; Gröbner basis; hyperfunction; identifiability index; input/output system; interconnection; matrix fraction description; minimal realization; multiplicity; regular system; state-space representation; time-varying linear system; transfer matrix; implicit systems; behaviours; finitely generated modules PDFBibTeX XMLCite \textit{S. Fröhler} and \textit{U. Oberst}, Syst. Control Lett. 35, No. 2, 97--110 (1998; Zbl 0909.93041) Full Text: DOI References: [1] J.-E. 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