Robust regulation in the presence of norm-bounded uncertainty

We consider robust regulation (against steps and sinusoids) in the presence of unstructured uncertainty. The unstructured uncertainty is norm bounded by a constant that is given a priori. This problem is equivalent to a certain multiobjective problem where one objective is robust regulation and the other is the standard objective of H_∞ suboptimal control. It is shown that a solution to this problem exists if and only if the standard H_∞ problem admits a solution and certain matrix inequalities are satisfied. These solvability conditions are readily computable. Controller synthesis is also addressed