Conjugation and model-matching in H∞

The author introduces a novel notion of conjugation and uses it to develop a unified framework of model matching and H^∞ control in the state space. The conjugation covers a wide range of algebraic operations including the inner-outer factorization of invertible systems. A special class of conjugations, the J-lossless conjugation, is regarded as a state-space representation of the classical interpretation problem. A model-matching problem is solved on the basis of the J-Lossless conjugation. The Pick matrix is represented in the state space as a solution to a Lyapunov-type equation, and its integral formula is derived, demonstrating a direct relation between the Pick matrix and the solution to the model-matching problem. The results are used to obtain a simple H^∞-controller