All solutions to the four block general distance problem

Abstract
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 Author(s) Limebeer, D.J.N. Dept. of Electr. Eng., Imperial Coll., London, UK Kasenally, E.M. ; Jaimoukha, I. ; Safonov, M.G.