The design of robustly performing controllers for an important class of control problems is treated. The problem is dealt with in the structured singular value (mu)-framework. The systems considered are characterized by weak nonlinearities and parametric and unstructured uncertainties. Nonlinear effects are taken into account via linearization families. Parametric uncertainty is included in a non-conservative way. Both lead to a mu-synthesis problem with repeated scalar real perturbations. As no direct solution to such a mu-synthesis problem is known to date, an iterative approach comprising both mu-analysis of the actual problem and D-K-iteration for a modified problem is shown. This approach is applied to a realistic continuous stirred-tank reactor for production of cyclopentenol to show the applicability to non-trivial MIMO process control problems.