KRYLOV SUBSPACE METHODS FOR SOLVING LARGE LYAPUNOV EQUATIONS

Published versio

Implicitly restarted Krylov subspace methods for stable partial realizations

Published versio

A Characterization of all Solutions to the Four Block General Distance Problem

All solutions to the four block general distance problem which arises in H^∞ optimal control are characterized. The procedure is to embed the original problem in an all-pass matrix which is constructed. It is then shown that part of this all-pass matrix acts as a generator of all solutions. Special attention is given to the characterization of all optimal solutions by invoking a new descriptor characterization of all-pass transfer functions. As an application, necessary and sufficient conditions are found for the existence of an H^∞ optimal controller. Following that, a descriptor representation of all solutions is derived

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