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

In this paper, an optimization method of low order multivariable controllers for H_infin control is proposed. Starting from a low order stabilizing controller, our proposed method gives a sequence of controllers for which the H_infin 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 H_infin criterion on the frequency domain. Numerical examples show that when the order is very low, the H_infin performance index is made much smaller than that of the initial controller that is obtained from the full order H_infin controller by a model reduction method. Our method gives better solutions than the initial controllers obtained by other local search methods.