On optimal robust disturbance attenuation

Abstract

In this article, we give an explicit solution to the nonstandard H ∞ problem which includes the optimal robust disturbance attenuation problem and the two-disc problem. The solution depends on an operator which is analogous to the Sarason operator for the standard H ∞ problem, it allows 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. Surprisingly, relatively little work has been done on it despite the large number of papers in the H ∞ control literature.