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Conference Papers Year : 2021

Bézout Identity in Pseudoratoinal Transfer Functions

Identités de Bézout pour des fonctions de transfert pseudo-rationnelles

Abstract

Coprime factorizations of transfer functions play various important roles, e.g., minimality of realizations, stabilizability of systems, etc. This paper studies the Bézout condition over the ring E (R −) of distributions of compact support and the ring M(R −) of measures with compact support. These spaces are known to play crucial roles in minimality of state space representations and controllability of behaviors. We give a detailed review of the results obtained thus far, as well as discussions on a new attempt of deriving general results from that for measures. It is clarified that there is a technical gap in generalizing the result for M(R −) to that for E (R −). A detailed study of a concrete example is given.
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Dates and versions

hal-03158705 , version 1 (04-03-2021)

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Cite

Yutaka Yamamoto, Catherine Bonnet. Bézout Identity in Pseudoratoinal Transfer Functions. MTNS 2021 -24th International Symposium on Mathematical Theory of Networks and Systems, Aug 2021, Cambridge, United Kingdom. ⟨10.1016/j.ifacol.2021.06.153⟩. ⟨hal-03158705⟩
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