In the H^∞ output feedback problem, there are two types of central controllers, which play a central role in characterizing all controllers achieving disturbance attenuation in the sense of the H^∞-norm.
In this paper, we provide a unified game-theoretic interpretation to the both types of central controllers. By employing completing the square argument of particular quadratic forms, we clarify that the two types of central controllers form different saddle points together with the corresponding worst-case disturbances. In the derivation of each saddle point, the difference is in the particular choice of quadratic-form functionals to which we apply the completing the square argument.
Then generalizing the approaches established here, we secondly consider a mixed attenuation problem of disturbances and initial-uncertainties. The trade-off between the attenuating the disturbances and the initial-uncertainties are characterized by the solution to the filtering Riccati equation.