An Iterative Algorithm for the Mixed H2/h∞ Control Problem Using H2 Norm Decreasing Controller Sets

This paper is concerned with the mixed H2/H∞ control problem. The purpose of this paper is to give an iterative algorithm for finding a sub-optimal static state feedback controller for the mixed H2/H∞ control problem. The key idea of our algorithm is to construct two “controller sets”: one is a set of controllers that improve the H2 norm of the closed loop map for a given controller and the other is a set of controllers whose elements satisfy the H∞ norm constraint. Using two controller sets, we propose an iterative algorithm. The obtained controller is either the global optimal solution if the H∞ norm constraint is satisfied until the H2 norm of the objective closed loop map converges to the H2 optimal value or a sub-optimal solution on the boundary of the H∞ norm constraint.