Coprimeness of Fractional Representations

Catherine Bonnet 1, 2 Yutaka Yamamoto 3, 4
1 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 : Coprimeness of a fractional representation plays various crucial roles in many different contexts, for example, stabilization of a given plant, minimality of a state space representation, etc. It should be noted however that coprimeness depends crucially on the choice of a ring (or algebra) where such a representation is taken, which reflects the choice of a plant, and particular problems that one studies. Such relationships are particularly delicate and interesting when dealing with infinite-dimensional systems. This paper discusses various coprimeness issues for different rings, typically for Hinfinity and pseudorational transfer functions. The former is related to Hinfinity-stabilizability, and the latter to controllability of behaviors. We also give some intricate examples where a seemingly non-coprime factorization indeed turns out to be a coprime factorization over Hinfinity. Some future directions are also indicated.
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Communication dans un congrès
55th IEEE Conference on Decision and Control, Dec 2016, Las Vegas, United States
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Contributeur : Catherine Bonnet <>
Soumis le : vendredi 23 décembre 2016 - 15:59:23
Dernière modification le : vendredi 17 février 2017 - 16:10:34
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  • HAL Id : hal-01413310, version 1

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Catherine Bonnet, Yutaka Yamamoto. Coprimeness of Fractional Representations. 55th IEEE Conference on Decision and Control, Dec 2016, Las Vegas, United States. <hal-01413310>

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