Stabilizability and stabilization of a rotating body-beam system with torque control

The stabilizability and stabilization of a rotating body-beam system with torque control are discussed. This system has a linear inertial manifold. An operator-theoretic argument is used to provide an alternative proof of this fact. By taking into account the effect of damping (structural or viscous), the stability result of J. Baillieul and M. Levi (1987) is proved using the LaSalle principle (1968). It is shown that there exists a critical angular velocity for the use of torque control to stabilize the system in the neutral configuration with constant angular velocity. For any constant angular velocity smaller than the critical one a feedback torque control law is given which exponentially strongly stabilizes the system in the neutral configuration with the system rotating at the given constant angular velocity