Synthesis of H∞ controllers based on conjugation

The authors consider the state-space characterization of the model-matching problem in H^∞. A simple characterization of the solutions is derived in the most general form, which covers the four-block problem, based on the notion of J-lossless conjugation. The derivation is elementary, simple, and straightforward, and it demonstrates that conjugation is a powerful tool for treating the model-matching problem in its most general form. The results are applied to the H^∞ control problem to yield a simple controller with order identical to that of the plant order. The controller and the closed-loop system obtained do not depend on the selection of the stabilizing matrices used for obtaining the comprime factorization