In this paper, we investigate the problem of robust synthesis of a static output feedback controller, with guaranteed quadratic 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 quadratic cost. Using a bisection method, this procedure is stopped when the controller reaches the best possible nominal performance that satisfies a given guaranteed quadratic cost. A numerical example shows the practical applicability of the proposed method.
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