Boundary null controllability of weakly coupled structurally damped beams

Julian Edward; Yacouba Simpore

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arXiv · 2609.07806

Boundary null controllability of weakly coupled structurally damped beams

Julian Edward·Yacouba Simpore

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Abstract

We prove boundary null controllability in any positive time for a finite system of Euler--Bernoulli beams with possibly non-diagonalizable coupling. For $0<\rho<2$, 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 $\rho=2$, an exact heat-system reduction gives the same result for $A=A^*\geq0$, despite the time-differential linkage of the reduced boundary inputs.

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Julian Edward, Yacouba Simpore. 2026-09-07. Boundary null controllability of weakly coupled structurally damped beams. https://arxiv.org/abs/2609.07806

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