The exponential stability of the vibration of two connected flexible arms by direct strain feedback control

Two uniform Euler-Bernoulli beams connected by a spring which models the vibration of two flexible arms is considered. It is shown that the direct strain feedback control which makes the closed-loop system of a single beam exponentially stable also works for current case when the spring mass is less than a fixed value. The closed-loop system is shown to be a Riesz system and the general condition for the exponential stability of the system is presented.