The mixed H2 /H∞ problem arises as one means to achieve robust good performance for a controlled linear time-invariant system. The idea is to achieve H2 optimal performance subject to an H∞ bound as robustness. It has been difficult to find good algorithms for solving this problem. In this study the problem was transformed into a bilinear matrix inequality problem (BMI). Solving the BMI by the method of centers was shown to be complicated by discontinuities resulting from the unobservability of the closed-loop system. Transforming the BMI problem into a lattice of BMI subproblems makes it possible to avoid the discontinuity and solve the original problem. A robust flight control system for the F-14 is included as an example of the algorithm.