Exponential stability of the Euler-Bernoulli beam with free ends by the Lyapunov function method

In this paper we consider the exponential stability of the Euler Bernoulli beam with free ends. Firstly, we prove the exponential stability of the Euler Bernoulli beam under boundary feedback control by the Lyapunov function method. Secondly, we design the Luenberger observer system by the observation signal. Then we construct the control based on the observer and obtain a closed-loop system. Finally, we prove that the closed-loop system is exponentially stable by constructing the appropriate Lyapunov function.