A new approach for robust fixed-order H-infinity controller design by convex optimization is proposed. Linear time-invariant single-input single-output systems represented by nonparametric models in the frequency domain are considered. It is shown that the H-infinity robust performance condition can be represented by a set of linear or convex constraints with respect to the parameters of a linearly parameterized controller in the Nyquist diagram. Systems with time-delay and with multimodel and frequency-domain uncertainty can be considered straightforwardly in the proposed approach. The proposed method is compared with the standard H-infinity control problem by a simulation example on an unstable system. (C) 2010 Elsevier Ltd. All rights reserved.