Abstract
Although there are many studies on the H∞ control, little is known about structures of H∞ state feedback controllers. In this paper we first correct the parametrization of H∞ controllers of the FI problem derived by DGKF since they has not parametrized a null space of T3. At the same time we also show an elementary proof of the necessary condition of the FI problem which only use the Nehari Theorem rather than the Hankel-Toeplitz operator. Using the result, we next parametrize the H∞ state feedback controllers and explain how dynamical free parameters implied in the H∞ controller are related with constant feedback gains which are different from the central solution F∞. Finally we derive some property of the Riccati equation associated with the central solution.
