A new approach is presented for designing multivariable PI-controllers, which are robust according to structural as well as parametrical model uncertainties. The algorithm starts with the regulator design by means of the well known optimal control procedure ignoring the model uncertainties. Then the input-output behaviour of the closed-loop original system is approximated using a majorization of the model error. It is shown, that the robustness requirements provide certain limitations on the controller matrix and hence on the weighting matrices in the performance index. These results lead to an instructive design algorithm to find a compromise between the fulfilment of the given requirements on the input-output behaviour and the robustness properties according to the model uncertainties.