A new combined analysis and synthesis procedure that provides a less conservative robust control design technique for systems with real parametric uncertainty is presented. The robust stability for these systems is analysed by the passivity theorem with generalized multipliers, and the worst case H-2 performance is investigated using an upper bound on the total output energy. The dynamics of the multipliers are systematically chosen using knowledge from the linear part of the uncertain systems. This approach provides additional degrees of freedom in the synthesis that lead to a reduction of the conservatism in the worst-case H-2 performance and achieved robustness bounds. However, the formulation of the control design problem is very complicated and it is difficult to solve directly. This paper presents an iterative algorithm, which in an H-2 equivalent of the D-K iteration for the mu/K-m synthesis, to account for the complicated couplings in the synthesis problem. We use a simple beam system with an uncertain modal frequency to illustrate that this synthesis technique with generalized multipliers results in less conservative controllers than previously published Popov controller synthesis techniques. In the process, we demonstrate that this design approach is very effective and simple to implement numerically.