Multi-objective H-infinity/H-infinity-synthesis with structured control laws is discussed and used as a means to enhance robustness of the system in the presence of real parametric uncertainty. NP-hardness of the computation of the structured singular value mu excludes its use within an optimisation procedure and raises the question of how to replace it. We show that the semi-structured distance to instability can be used for that purpose and we indicate how the resulting mixed H-infinity program can be solved efficiently. The method is applied to the regulation of a flexible geostationary satellite.