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...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Published: |
Springer
2021
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/94435/ https://link.springer.com/article/10.1007/s10883-021-09587-6 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| id |
my.upm.eprints.94435 |
|---|---|
| record_format |
eprints |
| spelling |
my.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 |
| institution |
Universiti Putra Malaysia |
| building |
UPM Library |
| collection |
Institutional Repository |
| continent |
Asia |
| country |
Malaysia |
| content_provider |
Universiti Putra Malaysia |
| content_source |
UPM Institutional Repository |
| url_provider |
http://psasir.upm.edu.my/ |
| 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. |
| format |
Article |
| author |
Azamov, Abdulla Ibragimov, Gafurjan Mamayusupov, Khudoyor Ruziboev, Marks |
| spellingShingle |
Azamov, Abdulla Ibragimov, Gafurjan Mamayusupov, Khudoyor Ruziboev, Marks On the stability and null-controllability of an infinite system of linear differential equations |
| author_facet |
Azamov, Abdulla Ibragimov, Gafurjan Mamayusupov, Khudoyor Ruziboev, Marks |
| author_sort |
Azamov, Abdulla |
| title |
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_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_sort |
on the stability and null-controllability of an infinite system of linear differential equations |
| publisher |
Springer |
| publishDate |
2021 |
| url |
http://psasir.upm.edu.my/id/eprint/94435/ https://link.springer.com/article/10.1007/s10883-021-09587-6 |
| _version_ |
1762394219468554240 |
| score |
13.160551 |