Optimization over H∞

The subject of H
^∞
control (as well as other branches of engineering) leads directly to sup norm optimization of rather general functionals on H
^∞
. This article surveys the known qualitative and quantitative results on such optimization problems. Our emphasis is on highly nonlinear performance criteria which lead to problems that are not accessible to the established techniques of Adamajan-Arov-Krein, Glover, and Foias-Nagy, Sarason.