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arXiv · 2506.10500

Boundary output feedback stabilization of a cascade of N heat equations

Hugo Lhachemi·Christophe Prieur·Emmanuel Trélat
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Abstract

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.

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Hugo Lhachemi, Christophe Prieur, Emmanuel Trélat. 2025-06-12. Boundary output feedback stabilization of a cascade of N heat equations. https://arxiv.org/abs/2506.10500

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