Stability Analysis for an Euler-Bernoulli Beam under Local Internal Control and Boundary Observation

In this paper, an Euler-Bernoulli beam system under the local internal distributed control and a boundary point observation is studied. We design an infinite-dimensional observer for the open-loop system. The closed loop-system that is non-dissipative is obtained by estimated state feedback. By a detailed spectral analysis, it is shown that there is a set of generalized eigenfunctions, which forms a Riesz basis for the state space. As consequences, both the spectrum-determined growth condition and exponential stability are concluded.