On optimal robust disturbance minimization

We give an explicit solution to the nonstandard H^∞ problem which includes the optimal robust disturbance attenuation problem and the two-disc problem. Our solution depends on an interplay among the function theory, Banach space duality and operator theory. The solution depends on an operator which is analogous to the Sarason operator for the standard H^∞ problem. This operator allows one to quantify the optimal performance of feedback systems and provides an explicit formula for the optimal controller. The nonstandard H^∞ problem is perhaps the simplest control problem which deals with significant plant uncertainty. Relatively little work has been done on it despite the large number of papers in the H^∞ control literature