# On the Baer extension problem for multidimensional linear systems

Abstract : Within an algebraic analysis approach, the purpose of the paper is to constructively solve the following problem: given two fixed multidimensional linear systems $S_1$ and $S_2$, parametrize the multidimensional linear systems $S$ which contain $S_1$ as a subsystem and satisfy that $S/S_1$ is isomorphic to $S_2$. In order to study this problem, we use Baer's classical interpretation of the extension functor and give an explicit characterization and parametrization of the equivalence classes of multidimensional linear systems $S$ solving this problem. We then use these results to parametrize the equivalence classes of multidimensional linear systems $S$ which admit a fixed parametrizable subsystem $S_1$ and satisfy that $S/S_1$ is isomorphic to a fixed autonomous system $S_2$. We illustrate the main results by means of explicit examples of differential time-delay systems.
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https://hal.inria.fr/inria-00175272
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Submitted on : Thursday, September 27, 2007 - 4:55:11 PM
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• HAL Id : inria-00175272, version 2

### Citation

Alban Quadrat, Daniel Robertz. On the Baer extension problem for multidimensional linear systems. [Research Report] RR-6307, INRIA. 2007, pp.43. ⟨inria-00175272v2⟩

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