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Partial numerical optimization of low order H∞ controller on the frequency domain

In this paper, an optimization method of low order multivariable controllers for Hinfin control is proposed. Starting from a low order stabilizing controller, our proposed method gives a sequence of controllers for which the Hinfin norm performance index is monotonically non-increasing where the tuning parameters are the coefficient matrices C and D of the low order controller with the matrices A and B being fixed at those of the initial controller. The proposed method is a descent method where the feasible direction is calculated by solving a linear matrix inequality that represents a sufficient condition for the Hinfin criterion on the frequency domain. Numerical examples show that when the order is very low, the Hinfin performance index is made much smaller than that of the initial controller that is obtained from the full order Hinfin controller by a model reduction method. Our method gives better solutions than the initial controllers obtained by other local search methods.