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Bézout Identity in Pseudoratoinal Transfer Functions

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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Contributor : Catherine Bonnet <>
Submitted on : Thursday, March 4, 2021 - 9:49:12 AM
Last modification on : Tuesday, April 13, 2021 - 12:20:16 PM


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  • HAL Id : hal-03158705, version 1


Yutaka Yamamoto, Catherine Bonnet. Bézout Identity in Pseudoratoinal Transfer Functions. MTNS 2020 - 24th International Symposium on Mathematical Theory of Networks and Systems, Aug 2021, Cambridge, France. ⟨hal-03158705⟩



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