Feedback stabilization: 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, it is important to have an operation that preserves that property i.e., a suitable blending method. In this paper we show that one can define a special blending that preserves stability and it is defined directly in terms of the plant and controller, without the necessity to use any factorization. Moreover, as an interesting side effect of these investigations, an operation is given that leaves invariant the strongly stabilizing controllers and defines a group structure on them, too.The properties of the newly defined operation are illustrated through the special case of static state feedback controllers. Besides its educative value the presentation also provides a possible tool for the algorithmic development.