Boundary null controllability of weakly coupled structurally damped beams
Abstract
We prove boundary null controllability in any positive time for a finite system of Euler--Bernoulli beams with possibly non-diagonalizable coupling. For 0<ρ<2, a Fourier--Jordan reduction yields a vector moment problem with polynomial--exponential modes. Under the Fattorini--Hautus condition, global spectral non-collision, and nonvanishing modal transfer factors, a suitably estimated block-biorthogonal family produces an H2 boundary control. Geometric multiplicities of the coupling matrix determine the minimal control dimension, and Jordan-block lengths determine the degrees of the generalized moments. At ρ=2, an exact heat-system reduction gives the same result for A=A*≥0, despite the time-differential linkage of the reduced boundary inputs.
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BibTeX
@misc{edward2026boundary,
title = {{Boundary null controllability of weakly coupled structurally damped beams}},
author = {Julian Edward and Yacouba Simpore},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07806},
eprint = {2609.07806},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07806},
}
RIS
TY - UNPB
TI - Boundary null controllability of weakly coupled structurally damped beams
AU - Julian Edward
AU - Yacouba Simpore
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07806
UR - https://arxiv.org/abs/2609.07806
AB - We prove boundary null controllability in any positive time for a finite system of Euler--Bernoulli beams with possibly non-diagonalizable coupling. For 0<ρ<2, a Fourier--Jordan reduction yields a vector moment problem with polynomial--exponential modes. Under the Fattorini--Hautus condition, global spectral non-collision, and nonvanishing modal transfer factors, a suitably estimated block-biorthogonal family produces an H^2 boundary control. Geometric multiplicities of the coupling matrix determine the minimal control dimension, and Jordan-block lengths determine the degrees of the generalized moments. At ρ=2, an exact heat-system reduction gives the same result for A=A^*≥0, despite the time-differential linkage of the reduced boundary inputs.
ER -