Design of fixed structural controller satisfying robust performance condition on Nyquist diagram

A new approach for the robust fixed-order H_∞ controller design by convex optimization is proposed. In this paper, the robust performance condition is represented by a set of convex constraints with respect to the parameters of a linearly parameterized controller on the Nyquist diagram for prespecified frequency points. This method can directly handle frequency-domain uncertainty without any modeling. Frequency-domain uncertainty can be minimized by selecting the appropriate nominal plant model for the corresponding frequency points in the proposed method. The proposed method is compared with the standard H_∞ control problem by experiments.