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.
Domains
Symbolic Computation [cs.SC]
Origin : Files produced by the author(s)
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