Stabilization of a Timoshenko beam system with a tip mass under unknown non-uniformly bounded disturbances

Abstract This paper addresses the boundary stabilization problem of a Timoshenko beam system with a tip mass under the external disturbance at the control end. Applying the idea of active disturbance rejection control, time-varying high-gain observers are designed to estimate the disturbances, and continuous anti-disturbances feedback controllers are developed. By choosing a suitable time-varying function, the disturbance error estimations can converge exponentially to zero. The well posedness of the closed-loop system is proved using the semigroup theory. With the proposed controllers, the exponential stability of the closed-loop system is demonstrated by constructing appropriate Lyapunov functional. A numerical simulation is given to illustrate the effectiveness of the proposed control strategy.