The boundary control problem of a cantilever Euler-Bernoulli beam with input time delay is considered.In order to exponentially stabilize the system, a feedback controller is adopted.And we study the well-posedness and exponential stability of the closed-loop system.The approach used in this paper is done by several steps.Firstly, the well-posedness of this system is proved by semi-group theory.Secondly, the asymptotical expression of eigenvalue is investigated by spectral analysis.Thirdly, the exponential stability of the system is studied by multiplier technology.Finally, numerical simulations on the dynamical behavior of the system are given to support the results obtained.
