Noncommutative geometric structures on stabilizable infinite-dimensional linear systems

Alban Quadrat 1, 2
1 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : This paper aims at showing that noncommutative geometric structures such as connections and curvatures exist on internally stabilizable infinite-dimensional linear systems and on their stabilizing controllers. To see this new geometry, using the noncommutative geometry developed by Connes, we have to replace the standard differential calculus by the quantized differential calculus and classical vector bundles by projective modules. We give an explicit description of the connections on an internally stabilizable system and on its stabilizing controllers in terms of the projectors of the closed-loop system classically used in robust control. These connections aim at studying the variations of the signals in the closed-loop system in response to a disturbance or a change of the reference. We also compute the curvatures of these connections.
Type de document :
Communication dans un congrès
ECC 2014, Jun 2014, Strasbourg, France. Proceedings of the European Control Conference 2014, pp.2460 - 2465, 2014, 〈10.1109/ECC.2014.6862563〉
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https://hal-supelec.archives-ouvertes.fr/hal-01108019
Contributeur : Myriam Baverel <>
Soumis le : jeudi 22 janvier 2015 - 09:28:50
Dernière modification le : jeudi 5 avril 2018 - 12:30:23

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Alban Quadrat. Noncommutative geometric structures on stabilizable infinite-dimensional linear systems. ECC 2014, Jun 2014, Strasbourg, France. Proceedings of the European Control Conference 2014, pp.2460 - 2465, 2014, 〈10.1109/ECC.2014.6862563〉. 〈hal-01108019〉

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