Boundary output feedback stabilization of a cascade of N heat equations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912426745659392 |
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| author | Lhachemi, Hugo Prieur, Christophe Trélat, Emmanuel |
| author_facet | Lhachemi, Hugo Prieur, Christophe Trélat, Emmanuel |
| contents | This paper solves the problem of output feedback stabilization for a cascade of N heat equations that are coupled at the boundary, the input being a scalar boundary control applied to the first heat equation of the cascade, and the scalar output being either a distributed or a pointwise in-domain measurement done on the last equation of the cascade. Two different configurations are studied in details. The first one consists of a cascade of N heat equations with totally disconnected spectra. The second one consists of a cascade of N identical heat equations, inducing eigenvalues of multiplicity N . In both cases, the problem is solved thanks to a spectral analysis and a study of the modal controllability and observability properties. The key point is that the generalized eigenvectors form a Riesz basis of the state space. The stabilization property is established in L^2 and H^1 norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10500 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary output feedback stabilization of a cascade of N heat equations Lhachemi, Hugo Prieur, Christophe Trélat, Emmanuel Optimization and Control This paper solves the problem of output feedback stabilization for a cascade of N heat equations that are coupled at the boundary, the input being a scalar boundary control applied to the first heat equation of the cascade, and the scalar output being either a distributed or a pointwise in-domain measurement done on the last equation of the cascade. Two different configurations are studied in details. The first one consists of a cascade of N heat equations with totally disconnected spectra. The second one consists of a cascade of N identical heat equations, inducing eigenvalues of multiplicity N . In both cases, the problem is solved thanks to a spectral analysis and a study of the modal controllability and observability properties. The key point is that the generalized eigenvectors form a Riesz basis of the state space. The stabilization property is established in L^2 and H^1 norms. |
| title | Boundary output feedback stabilization of a cascade of N heat equations |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2506.10500 |