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Bézout Identity in Pseudoratoinal Transfer Functions
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.
https://hal.inria.fr/hal-03158705
Contributor : Catherine Bonnet Connect in order to contact the contributor
Submitted on : Thursday, March 4, 2021 - 9:49:12 AM
Last modification on : Friday, February 4, 2022 - 3:14:02 AM
Long-term archiving on: : Saturday, June 5, 2021 - 6:25:32 PM
Contributor : Catherine Bonnet Connect in order to contact the contributor
Submitted on : Thursday, March 4, 2021 - 9:49:12 AM
Last modification on : Friday, February 4, 2022 - 3:14:02 AM
Long-term archiving on: : Saturday, June 5, 2021 - 6:25:32 PM
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MTNS20__YYCB.pdf
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