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Equivalences of linear functional systems

Thomas Cluzeau 1 Alban Quadrat 2
2 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : Within the algebraic analysis approach to linear systems theory, we investigate the equivalence problem of linear functional systems, i.e., the problem of characterizing when all the solutions of two linear functional systems are in a one-to-one correspondence. To do that, we first provide a new characterization of isomorphic finitely presented modules in terms of inflations of their presentation matrices. We then prove several isomorphisms which are consequences of the unimodular completion problem. We then use these isomorphisms to complete and refine existing results concerning Serre's reduction problem. Finally, different consequences of these results are given. All the results obtained in this paper are algorithmic for rings for which Gröbner basis techniques exist and the computations can be performed by the Maple packages OreModules and OreMorphisms.
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https://hal.inria.fr/hal-01413593
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Submitted on : Saturday, December 10, 2016 - 12:48:19 AM
Last modification on : Wednesday, October 20, 2021 - 1:31:23 AM
Long-term archiving on: : Tuesday, March 28, 2017 - 12:26:29 AM

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  • HAL Id : hal-01413593, version 1
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Thomas Cluzeau, Alban Quadrat. Equivalences of linear functional systems. [Research Report] RR-9000, Inria Lille - Nord Europe; University of Limoges, France. 2016, pp.29. ⟨hal-01413593⟩

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