Balanced truncation preserving poles in a specified disk and it´s application to the reduction H∞ controller

In this paper, a model reduction method for a linear time invariant stable system whose poles are located in a specified disk on the complex left half plane is considered. This method is based on the balanced truncation technique that is often used for reducing a high order stable system to low order stable one. A number of properties of the balanced truncation technique are maintained. The error bound is evaluated using Hankel singular values of the original system. As one of applications of the method, the authors tackled a reduction problem of an H_∞ controller