A J-Spectral Factorization Approach to H∞ Control

Abstract

It is shown that necessary and sufficient conditions for the existence of sub-optimal solutions to the model matching problem associated with H∞ control are that two coupled J-spectral factorizations exist. The second J-spectral factor provides a parameterization of all solutions to the model matching problem. The existence of the J-spectral factors is then shown to be equivalent to the existence of stabilizing, non-negative definite solutions to two algebraic Riccati equations, allowing a state-space formula for a linear fractional representation of all controllers to be given.