The general H∞ problem with static output feedback

In this paper we shall consider the H_∞ control problem using static output feedback. Recently, this problem was solved in the regular case. We shall extend this result such that no assumption concerning the direct feedthrough term in the H_∞ problem is made. The main result states that the H_∞ static output feedback control problem is solvable if and only if the general H_∞ static state feedback problem is solvable and, further, that a certain ´geometric Riccati type´ side constraint is satisfied.