  This paper is concerned with the output feedback exponential stabilization
for a flexible beam with tip mass. When there is no disturbance, it is shown
that only one non-collocated measurement is enough to exponentially stabilize
the original system by constructing an infinite-dimensional Luenberger state
observer to track the state and designing an estimated state based output
feedback control law. This essentially improves the existence result in [F.
Conrad and O. M\"{o}rg\"{u}l, SIAM J. Control Optim., 36 (1998), 1962-1986]
where two collocated measurements including high order feedback were adopted.
In the case that boundary internal uncertainty and external disturbance are
considered, an infinite-dimensional disturbance estimator is constructed to
estimate the state and total disturbance in real time. By virtue of the
estimated state and estimated total disturbance, an output feedback control law
is designed to exponentially stabilize the original system while guaranteeing
the boundedness of the closed-loop system. Some illustration simulations are
presented.

Optimization and Control