Article Dans Une Revue Linear Algebra and its Applications Année : 2025

Interplay between discretization and controllability of linear delay systems: an algebraic viewpoint

Résumé

In this paper, we give an in depth study of linear delay systems controllability preservation/alte- ration through discretization. We make use of a module theoretic framework acting as a unifying one for most of the existing delay system controllability notions. We propose a formal generic definition of a discretization scheme and illustrate through examples that controllability properties may be lost through discretization. Then, we introduce the notion of preservation (that is, a measure of quantifying the ability of the discretizer to preserve controllability properties) and prove that for a given discretizer, we can always find a delay system for which even the torsion-free controllability (which is the weakest controllability notion) is not preserved. Finally, we reverse the situation, and show that for any given delay system, preserving discretizers exist.

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hal-04976874 , version 1 (29-09-2025)

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Florentina Nicolau, Hugues Mounier, Silviu-Iulian Niculescu. Interplay between discretization and controllability of linear delay systems: an algebraic viewpoint. Linear Algebra and its Applications, 2025, 713, pp.18-73. ⟨10.1016/j.laa.2025.02.025⟩. ⟨hal-04976874⟩
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