Conjugation, interpolation and model-matching in<i>H</i>^∞

Abstract

Abstract The notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions. Two classes of conjugations are shown to be important. One is the lossless conjugation that performs inner-outer factorization and the other is the J-lossless conjugation that solves the model-matching problem related to H 8-control. The solution of the model-matching problem obtained by J-lossless conjugation is regarded as the state-space version of the directional interpolation theory, and is much simpler than those obtained via the Nehari approximation.