On robust two-block problems

In this paper we consider the following robust two-block problem that arises in estimation and in full-information control: minimize the worst-case H^∞ norm of a two-block transfer matrix whose elements contain H^∞-norm-bounded modeling errors. We show that, when the underlying systems are single-input/single-output, and if the modeling errors are “small enough”, then the robust, two-block problem can be solved by solving a one-dimensional family of appropriately-weighted “modeling-error-free” two-block problems. We also study the consequences of this result to a robust tracking problem, where the optimal solution can be explicitly found