Dynamic stabilization for a cascaded beam PDE–ODE system with boundary disturbance

Abstract

We are concerned with the dynamic stabilization for a cascaded Euler–Bernoulli beam (EBB) partial differential equation (PDE)–ordinary differential equation (ODE) system subject to boundary control and matched internal uncertainty and external disturbance. State feedback stabilization of such system without disturbance has been recently discussed by X.H. Wu, H. Feng (Sci China Inf Sci, 2022, 65(5): 159202). An infinite‐dimensional disturbance estimator is constructed in order to estimate the total disturbance. By compensating the total disturbance, we design a state observer to trace the state and then an estimated state and estimated total disturbance‐based output feedback control law. It is proved that the original system is exponentially stable, and other states of the closed‐loop are bounded. Some numerical simulations are presented.