Controllability and Stabilization of a Wave-Heat Cascade System
Optimization and Control
2025-06-13 v1
Abstract
Considering a wave-reaction-diffusion PDE cascade system with wave Neumann control, we first establish controllability properties in a suitable Hilbert space depending on the coupling cascade term. This is done by deriving an observability inequality for the dual problem by resorting to an Ingham-M{\"u}ntz inequality. Second, we design an explicit output feedback control strategy for the actual stabilization of the PDE cascade. The key property is that the underlying operator is a Riesz-spectral operator.
Cite
@article{arxiv.2506.10495,
title = {Controllability and Stabilization of a Wave-Heat Cascade System},
author = {Hugo Lhachemi and Christophe Prieur and Emmanuel Trélat},
journal= {arXiv preprint arXiv:2506.10495},
year = {2025}
}