Blending for H∞ performance: a group theoretic approach

In order to design efficient algorithms that work on the set of controllers that fulfill a given property, e.g., stability or a norm bound, it is important to have an operation that preserves that property, i.e., a suitable blending method. Concerning stability, a traditional approach is to use the Youla parametrization and the corresponding parameters as a starting point. While this method guarantees stabilizability as the invariant property for the fairly large class of strictly proper plants, there are also other solutions to the problem. The authors already provide a detailed analysis for feedback stability placing the controller blending problem in a general setting by pointing to the basic global geometric structures that are related to well-posedness and feedback stability. In this paper these efforts are continued and the group structure corresponding to performance problems, e.g., those related to a suboptimal H∞ design, is presented. Besides its educative value the presentation provides a possible tool for the algorithmic development.