  This paper is concerned with the point torque boundary feedback stabilization
of a damped Euler-Bernoulli beam model in the presence of a time-varying
state-delay. First, a finite-dimensional truncated model is derived by spectral
reduction. Then, for a given stabilizing state-feedback of the delay-free
truncated model, an LMI-based sufficient condition on the maximum amplitude of
the state-delay is employed to guarantee the stability of the closed-loop
state-delayed truncated model. Second, we assess the exponential stability of
the resulting closed-loop infinite-dimensional system under the assumption that
the number of modes of the original infinite-dimensional system captured by the
truncated model has been selected large enough. Finally, we consider in our
control design the possible presence of a distributed perturbation, as well as
additive boundary perturbations in the control inputs. In this case, we derive
for the closed-loop system an exponential input-to-state estimate with fading
memory of the distributed and boundary disturbances.
