The stabilization of an Euler-Bernoulli beam under boundary control and non-collocated observation

We study the stabilization of an Euler-Bernoulli equation under the boundary control at one end and observation at another end. We construct an infinite-dimensional observer to track the state exponentially. A proportional output feedback control based on the observed state is designed. The closed-loop system is shown to be non-dissipative but a Riesz spectral system. Then both the determined-growth condition and exponential stability are concluded.