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 gives superior performance while providing robustness to nonlinear plant/model mismatch. To the authors’ knowledge, the corresponding optimization problem is the largest BMI control problem ever solved.