Stabilization of a rotating body–beam by output feedback torque control

This paper deals with the output feedback stabilization problem for a rotating body–beam system, originally studied by Baillieul and Levi. Inspired by the work of Li and Xu, we design an observer to estimate the system state by measuring the boundary moment force of beam at root and the angular velocity of disk. A novel Lyapunov functional is developed to prove exponential convergence of the observer. Utilizing the observer in the control law designed by Coron and d’Andréa-Novel, we achieve local asymptotic stability of the closed-loop system. Our results present an example of applying the so-called separation principle to stabilize nonlinear infinite-dimensional systems, whose applicability is well-known to finite dimensional systems.