2025/06/12 by Hugo Lhachemi, Christophe Prieur, Lhachemi, Hugo +3
Engineering · #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2506.10500
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 L2 and H1 norms.