H∞ strong stabilization

This paper presents a technique for designing stableH1 controllers. Similar to some methods in the existing literature, the proposed method also uses the parameterization of all suboptimal H1 controllers so that the stable H1 design problem can be (conservatively) converted into another 2-block standard H1 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 signicantly reduced by a two-step reduction algorithm. Numerical examples are presented to demonstrate the eectiveness of the proposed method.

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