A Numerical Method for Scaled H∞ Control Problems Based on Approximation of Inverse of Positive Definite Matrix

$H_{\infty}$ control is one of the effective design methods for robust control systems and is significant in that it allows frequency shaping in the control system, but the design results are conservative when dealing with parameter as multiplicative uncertainties. The scaled $H_{\infty}$ control problem has been proposed as an approach to handle this problem, and an effective numerical solution method is the dual iteration method. While the dual iteration method efficiently improves the control performance, it also leads to numerical instability. Accordingly, a numerical method for the scaled $H_{\infty}$ problem that has numerical stability and high efficiency is needed. This paper proposes a numerical method for the scaled $H_{\infty}$ control problem based on the approximation of inverse matrices. This paper also shows the effectiveness of the proposed method through a numerical example.