Spectral determination for a cantilever beam

The eigenvalue specification problem is discussed for a beam with one end clamped and the other end free, which is allowed to have some structural damping, and has a moment force at the free end acting as a control. The spectrum and eigenvectors of the uncontrolled system are first analyzed and are then used to construct the feedback element which solves the problem. It is shown how this feedback element can be numerically approximated, and a spillover result is proved for the approximation. In the case where there is no damping, this method yields a bounded feedback law which exponentially stabilizes the beam