Exponential stabilization for an Euler–Bernoulli beam PDE-ODE cascade system

Abstract

We discuss the exponential stabilization for an Euler–Bernoulli beam (EBB) partial differential equation (PDE)-ordinary differential equation (ODE) cascaded system with actuator placing on the PDE boundary. In absence of internal uncertainty and external disturbance, we construct a state feedback controller in order to exponentially stabilize the considered system. In presence of internal uncertainty and external disturbance, we design an infinite-dimensional extended state observer to estimate the state and total disturbance simultaneously. An estimated state and estimated disturbance based controller is then constructed. It is proved that the original system is exponentially stable and the whole closed-loop system is bounded. Some numerical simulations are carried out to illustrate effectiveness of our proposed control strategy.