A computational approach is developed for designing a globally optimal controller which is
robust to time-varying nonlinear perturbations in the plant. This controller design problem is
formulated as an optimization with bilinear matrix inequality (BMI) constraints, and is solved
to optimality by a branch and bound algorithm. The algorithm is applied to a reactive ion
etcher, and provides superior performance while providing robustness to nonlinear
plant/model mismatch. The algorithm is also applied to a well known benchmark problem.