All solutions to the four block general distance problem

The authors characterize all solutions to the four-block general distance problem which arises in H^∞-optimal control. The procedure is to embed the original problem in an all-pass matrix constructed by the authors. It is then demonstrated that part of this all-pass matrix acts as a generator of all solutions. As an application, the authors find a representation formula for all solutions to H^∞-optimal control problems of the third kind