Exact solution to the non-standard H∞ problem

The non-standard H^∞ problem μ₀=inf _Q∈H∞|||W(1-P₀Q)|+|VP₀ Q|||_∞ plays a fundamental role in robust feedback control. Here we develop a new operator theoretic framework to characterize explicitly its solution. We also establish absolute continuity of a dual extremal measure showing that the optimal performance/controller satisfy an extremal identity, which provides a test of optimality. Moreover, via the Banach space duality theory we show existence of a maximal vector leading to an explicit formula for the optimal controller