Exponential Stability of the Euler-Bernoulli Beam Equation with External Disturbance and Output Feedback Time-Delay

This paper concerns the stability of a one-dimensional Euler-Bernoulli beam equation with external disturbance and output feedback time-delay, in which the disturbance is bounded by an exponential function. In order to estimate disturbance, the authors design an estimator of disturbance, which is composed of two parts: One is the system measurement that is called the eigen-measurement, another is a time-variant estimator of disturbance. Thus, the feedback controller which is based on the estimate of the disturbance is designed to stabilize the system. The finite-time stability of the system under this control law is proved by Lyapunov function method. Finally, some numerical simulations on the dynamical behavior of the closed-loop system is presented to show the correctness of the result.