On the stability and null-controllability of an infinite system of linear differential equations
In this work, the null controllability problem for a linear system in ℓ2 is considered, where the matrix of a linear operator describing the system is an infinite matrix with λ∈R on the main diagonal and 1s above it. We show that the system is asymptotically stable if and only if λ ≤− 1, which sho...
| Main Authors: | , , , |
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| Format: | Article |
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Springer
2021
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| _version_ | 1825937463096377344 |
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| author | Azamov, Abdulla Ibragimov, Gafurjan Mamayusupov, Khudoyor Ruziboev, Marks |
| author_facet | Azamov, Abdulla Ibragimov, Gafurjan Mamayusupov, Khudoyor Ruziboev, Marks |
| author_sort | Azamov, Abdulla |
| collection | UPM |
| description | In this work, the null controllability problem for a linear system in ℓ2 is considered, where the matrix of a linear operator describing the system is an infinite matrix with λ∈R
on the main diagonal and 1s above it. We show that the system is asymptotically stable if and only if λ ≤− 1, which shows the fine difference between the finite and the infinite-dimensional systems. When λ ≤− 1 we also show that the system is null controllable in large. Further we show a dependence of the stability on the norm, i.e. the same system considered ℓ∞
is not asymptotically stable if λ = − 1. |
| first_indexed | 2024-03-06T10:59:53Z |
| format | Article |
| id | upm.eprints-94435 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-03-06T10:59:53Z |
| publishDate | 2021 |
| publisher | Springer |
| record_format | dspace |
| spelling | upm.eprints-944352023-03-29T08:30:09Z http://psasir.upm.edu.my/id/eprint/94435/ On the stability and null-controllability of an infinite system of linear differential equations Azamov, Abdulla Ibragimov, Gafurjan Mamayusupov, Khudoyor Ruziboev, Marks In this work, the null controllability problem for a linear system in ℓ2 is considered, where the matrix of a linear operator describing the system is an infinite matrix with λ∈R on the main diagonal and 1s above it. We show that the system is asymptotically stable if and only if λ ≤− 1, which shows the fine difference between the finite and the infinite-dimensional systems. When λ ≤− 1 we also show that the system is null controllable in large. Further we show a dependence of the stability on the norm, i.e. the same system considered ℓ∞ is not asymptotically stable if λ = − 1. Springer 2021-12-23 Article PeerReviewed Azamov, Abdulla and Ibragimov, Gafurjan and Mamayusupov, Khudoyor and Ruziboev, Marks (2021) On the stability and null-controllability of an infinite system of linear differential equations. Journal of Dynamical and Control Systems. pp. 1-11. ISSN 1079-2724; ESSN: 1573-8698 https://link.springer.com/article/10.1007/s10883-021-09587-6 10.1007/s10883-021-09587-6 |
| spellingShingle | Azamov, Abdulla Ibragimov, Gafurjan Mamayusupov, Khudoyor Ruziboev, Marks On the stability and null-controllability of an infinite system of linear differential equations |
| title | On the stability and null-controllability of an infinite system of linear differential equations |
| title_full | On the stability and null-controllability of an infinite system of linear differential equations |
| title_fullStr | On the stability and null-controllability of an infinite system of linear differential equations |
| title_full_unstemmed | On the stability and null-controllability of an infinite system of linear differential equations |
| title_short | On the stability and null-controllability of an infinite system of linear differential equations |
| title_sort | on the stability and null controllability of an infinite system of linear differential equations |
| work_keys_str_mv | AT azamovabdulla onthestabilityandnullcontrollabilityofaninfinitesystemoflineardifferentialequations AT ibragimovgafurjan onthestabilityandnullcontrollabilityofaninfinitesystemoflineardifferentialequations AT mamayusupovkhudoyor onthestabilityandnullcontrollabilityofaninfinitesystemoflineardifferentialequations AT ruziboevmarks onthestabilityandnullcontrollabilityofaninfinitesystemoflineardifferentialequations |