Low‐order H∞ controller design on the frequency domain by partial optimization

In this paper, an optimization method of low‐order multivariable controllers for H_∞ control is proposed. Starting from a low‐order stabilizing controller, our method gives a sequence of controllers for which the H_∞ norm performance index is monotonically non‐increasing by tuning the numerator coefficient matrices of the low‐order controller. This controller class includes multivariable PID controllers. 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_∞ criterion for each frequency. Usefulness is shown by two numerical examples. Copyright © 2009 John Wiley & Sons, Ltd.