Rapid stabilization of general linear systems with F-equivalence
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915833937133568 |
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| author | Hayat, Amaury Loko, Epiphane |
| author_facet | Hayat, Amaury Loko, Epiphane |
| contents | We study the rapid stabilization of general linear systems, when the differential operator $\mathcal{A}$ has a Riesz basis of eigenvectors. We find simple sufficient conditions for the rapid stabilization and the construction of a relatively explicit feedback operator. We use an $F$-equivalence approach \textcolor{black}{relying on Fredholm transformation} to show a stronger result: under these sufficient conditions the system is equivalent to a simple exponentially stable system, with arbitrarily large decay rate. In particular, our conditions improve the existing conditions of rapid stabilization for non-parabolic operators such as skew-adjoint systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04031 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rapid stabilization of general linear systems with F-equivalence Hayat, Amaury Loko, Epiphane Analysis of PDEs We study the rapid stabilization of general linear systems, when the differential operator $\mathcal{A}$ has a Riesz basis of eigenvectors. We find simple sufficient conditions for the rapid stabilization and the construction of a relatively explicit feedback operator. We use an $F$-equivalence approach \textcolor{black}{relying on Fredholm transformation} to show a stronger result: under these sufficient conditions the system is equivalent to a simple exponentially stable system, with arbitrarily large decay rate. In particular, our conditions improve the existing conditions of rapid stabilization for non-parabolic operators such as skew-adjoint systems. |
| title | Rapid stabilization of general linear systems with F-equivalence |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.04031 |