Exact controllability and boundary stabilization of flexural vibrations of an internally damped flexible space structure

摘要

We consider a problem of flexural vibrations of a flexible rectangular panel, incorporating small internal damping of the material. The panel is hoisted by a rigid hub at one end and the other end totally free. For attachment of the rigid hub on one side of the panel, its dynamics leads to a nonstandard boundary condition and the whole system becomes a hybrid system of dynamics. The exact controllability theory is established using the Hilbert Uniqueness Method, by means of an active control applied only on the rigid hub. The uniform exponential decay of solution is also obtained directly for such formulation with viscous boundary damping at the hub end only.