The robust regulator problem for linear MIMO systems in the frequency domain is considered. The stability robustness of the overall system is analysed with respect to additive perturbations in the mathematical model of the plant, and a controller that has been designed to solve the regulator problem for the nominal plant Po(s). It is shown that in the special case where the reference signal (or the disturbance) has a pole at s =jωk, the robustness can be upper-bounded by the minimum singular value of Po(jωk). This upper bound can be achieved in the case of a stable plant and step reference and disturbance. A design procedure for obtaining>H∞ -optimal solutions is given.