A new robust controller design method is developed for linear time-invariant single-input single-output systems presented by their frequency response data. The performance specifications are in terms of the upper bounds on the infinity norm of weighted closed-loop frequency responses. The designed controller is robust in terms of frequency-domain disk and polytopic uncertainty as well as multimodel uncertainty. The necessary and sufficient conditions for the existence of such controllers are presented by a set of convex constraints. The practical issues to compute fixed-order rational H-infinity controllers by convex optimization techniques are discussed. The experimental results on an electromechanical system illustrate the effectiveness of the proposed method.