Output feedback stabilisation of an axially moving string subject to a spring-mass-dashpot

In this paper, we consider the output feedback stabilisation of an axially moving string system subject to a spring-mass-dashpot boundary condition. By constructing an invertible backstepping transformation, we design a state feedback controller to stabilise the system. Next, we present an observer to estimate the states of the system, and based on the estimated states, we design an output-feedback controller. The closed-loop system is proved to be exponentially stable by Lyapunov analysis. Numerical simulations are presented to verify the effectiveness of the proposed controller.