Controller blending - a geometric 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. While available approaches use the Youla parameters in order to define this operation for stability in a trivial way, they do not provide a general answer to the problem. This paper places the controller blending problem in a more general setting by pointing to the basic global geometric structures that are related to feedback stability or suboptimal ℋ_∞ design. A detailed analysis is given for feedback stability: an operation is given under which well-posedness is a group while stability is a semigroup. Moreover, an operation is given that makes controllers with strongly stable property a group.