Mixed H2/H∞ optimization: a BMI solution

The mixed H₂/H_∞ problem has received a great deal of attention. However, constrast to the upper bound problem, an optimal solution for this problem involving different performance measures is difficult to obtain. It is shown that this problem can be transformed into a BMI optimization problem. The method of centers is proposed to solve this BMI problem. However, the procedure involving the interior point algorithm does not always work because of the discontinuity of the BMI. Conditions under which the interior point algorithm will work are provided in this paper. Furthermore, it was found that the discontinuity is due to the unobservability of the closed-loop system. By analyzing the unobservable controlled invariants, the BMI problem can be transformed into a lattice of BMI subproblems. By traversing the lattice, the original BMI optimization problem can be solved