The control of a globally unstable boundary-layer flow along a two-dimensional cavity is considered. When perturbed by the worst-case initial condition, the flow exhibits a large transient growth associated with the development of a wave packet along the cavity shear layer followed by a global cycle related to the least stable global eigenmodes. The flow simulation procedure is coupled to a measurement feedback controller, which senses the wall shear stress at the downstream lip of the cavity and actuates at the upstream lip. A reduced model for the control optimization is obtained by a projection on the least stable global eigenmodes. The LQG controller is run in parallel to the Navier-Stokes time integration. It is shown that the controller is able to damp out the global oscillations.