The aim of this paper is to identify an LFT model with frequency-domain data. Under a left invertibility condition inputs and outputs of a real structured model perturbation Δ can be deduced from the measured inputs and outputs, so that Δ the model perturbation can be identified with a Robust Least Squares method or an output error set-membership identification technique. The influence of a controller on the sensitivity of the identification scheme, face to neglected dynamics, measurement noise and other disturbances acting on the closed loop is studied. Using a classical convex closed loop design technique, a controller that reduces this sensitivity while satisfying stability and performance requirements is synthesized. An illustrative example is given.