Duality in robust control: uncertainty vs. controller

To find a controller that provides the maximal stability margin to an LTI system under rank-one perturbations is a quasiconvex problem. In the paper, the dual quasiconvex problem is obtained, using the convex duality arguments in the Hardy space H^∞. It is shown that the dual problem can be viewed as minimization of a "length" of uncertainties that destabilize the system. Several examples establishing a connection with such classical results as the corona theorem and the Adamyan-Arov-Krein theorem are considered