$H2∕H∞$ Robust Static Output Feedback Control Design Without Solving Linear Matrix Inequalities

In this paper, we investigate the problem of robust synthesis of a static output feedback controller, with guaranteed $H2∕H∞$ cost, in the context of multiple parametric uncertainties. To solve this problem, a random optimization technique based on a bisection method is proposed. The principle is as follows: For a given initial stabilizing controller of the nominal system, the proposed approach iteratively generates a sequence of matrices with a decreasing $H2∕H∞$ cost. By a bisection method, this procedure is stopped when the controller reaches the best possible nominal performance that satisfies a given guaranteed $H2∕H∞$ cost. Numerical examples show the practical applicability of the proposed method.