H∞ strong stabilization

This note presents a technique for designing stable H-infinity controllers. Similar to some methods in the existing literature, the proposed method also uses the parameterization of all suboptimal H-infinity controllers so that the stable H-infinity design problem can be (conservatively) converted into another 2-block standard H-infinity problem. However, a weighting function is introduced in this method to alleviate the conservativeness of the previous formulations. It is further shown that the resulting high-order controller can be significantly reduced by a two-step reduction algorithm. Numerical examples are presented to demonstrate the effectiveness of the proposed method.