Stabilization of an Euler-Bernoulli Beam with a Tip Mass Under the Unknown Boundary External Disturbances

This paper studies the stabilization problem of an Euler-Bernoulli beam with a tip mass,which undergoes unknown but uniform bounded disturbance at tip mass. Here the nonlinear feedback control law is used to cancel the effects of the external disturbances. For the controlled nonlinear system,the authors prove the well-posedness by the maximal monotone operator theory and the variational principle. Further the authors prove that the controlled nonlinear system is exponential stable by constructing a suitable Lyapunov function. Finally, some numerical simulations are given to support these results.