Exponential stabilization for a flexible beam with tip rigid body subject to boundary non-linear disturbance

Abstract In this paper, we address the boundary output feedback exponential stabilization for a flexible beam with tip rigid body subject to non-linear disturbance. The exponential stabilization of such system without disturbance has been verified in Guo (2002, Optim. Method Softw., 17, 655–81), where three collocated measurements were used. With one collocated and two non-collocated measurements, we construct a new infinite-dimensional extended state observer to estimate the state and total disturbance online. The estimated state and the estimated disturbance are used to the design of stabilizing control law. Based on the well-known Riesz basis approach, we show that a coupled system including the original system is exponentially stable. Moreover, the boundedness of the whole closed-loop system is verified.