Static output feedback design for H∞ control by descent method

In this paper, a search method for a static output feedback gain of H
_∞
control problem is proposed. This method treats the bilinear matrix inequality that contains a Lyapunov matrix and a controller gain as variables directly. It is a descent method in the controller gain space. A feasible direction of the gain is obtained by solving a linear matrix inequality and a minimum point in the direction is found by a line search. By the iteration of this procedure, a monotonically non-increasing sequence of H
_∞
norm is given