A corona theorem for an algebra of Radon measures with an application to exact controllability for linear controlled delayed difference equations
This paper proves a corona theorem for the algebra of Radon measures compactly supported in $\mathbb{R}_-$ and this result is applied to provide a necessary and sufficient Hautus–type frequency criterion for the $L^1$ exact controllability of linear controlled delayed difference equations (LCDDE). H...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-10-01
|
| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.604/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206157392740352 |
|---|---|
| author | Fueyo, Sébastien Chitour, Yacine |
| author_facet | Fueyo, Sébastien Chitour, Yacine |
| author_sort | Fueyo, Sébastien |
| collection | DOAJ |
| description | This paper proves a corona theorem for the algebra of Radon measures compactly supported in $\mathbb{R}_-$ and this result is applied to provide a necessary and sufficient Hautus–type frequency criterion for the $L^1$ exact controllability of linear controlled delayed difference equations (LCDDE). Hereby, it solves an open question raised in [5]. |
| format | Article |
| id | doaj-art-642736790e774482912b4ee905b5b07a |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-642736790e774482912b4ee905b5b07a2025-02-07T11:22:49ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-10-01362G885186110.5802/crmath.60410.5802/crmath.604A corona theorem for an algebra of Radon measures with an application to exact controllability for linear controlled delayed difference equationsFueyo, Sébastien0Chitour, Yacine1School of Electrical Engineering-Systems, Tel Aviv University, Tel Aviv, Israel 69978Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des signaux et systèmes, 91190, Gif-sur-Yvette, France.This paper proves a corona theorem for the algebra of Radon measures compactly supported in $\mathbb{R}_-$ and this result is applied to provide a necessary and sufficient Hautus–type frequency criterion for the $L^1$ exact controllability of linear controlled delayed difference equations (LCDDE). Hereby, it solves an open question raised in [5].https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.604/Corona theorem, Bézout’s identitydifference delay equationsexact controllability |
| spellingShingle | Fueyo, Sébastien Chitour, Yacine A corona theorem for an algebra of Radon measures with an application to exact controllability for linear controlled delayed difference equations Comptes Rendus. Mathématique Corona theorem, Bézout’s identity difference delay equations exact controllability |
| title | A corona theorem for an algebra of Radon measures with an application to exact controllability for linear controlled delayed difference equations |
| title_full | A corona theorem for an algebra of Radon measures with an application to exact controllability for linear controlled delayed difference equations |
| title_fullStr | A corona theorem for an algebra of Radon measures with an application to exact controllability for linear controlled delayed difference equations |
| title_full_unstemmed | A corona theorem for an algebra of Radon measures with an application to exact controllability for linear controlled delayed difference equations |
| title_short | A corona theorem for an algebra of Radon measures with an application to exact controllability for linear controlled delayed difference equations |
| title_sort | corona theorem for an algebra of radon measures with an application to exact controllability for linear controlled delayed difference equations |
| topic | Corona theorem, Bézout’s identity difference delay equations exact controllability |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.604/ |
| work_keys_str_mv | AT fueyosebastien acoronatheoremforanalgebraofradonmeasureswithanapplicationtoexactcontrollabilityforlinearcontrolleddelayeddifferenceequations AT chitouryacine acoronatheoremforanalgebraofradonmeasureswithanapplicationtoexactcontrollabilityforlinearcontrolleddelayeddifferenceequations AT fueyosebastien coronatheoremforanalgebraofradonmeasureswithanapplicationtoexactcontrollabilityforlinearcontrolleddelayeddifferenceequations AT chitouryacine coronatheoremforanalgebraofradonmeasureswithanapplicationtoexactcontrollabilityforlinearcontrolleddelayeddifferenceequations |