Does robust regulation compromise H2 performance?

The authors consider the problem of minimizing the H₂ norm of a feedback system subject to the constraint that the controller regulate robustly against constants and sinusoids. They show that for any ∈>0, there exists a controller that both achieves regulation and renders the closed-loop H₂ norm within ∈ of the optimal norm (the norm achievable without the regulation constraint). Necessary and sufficient conditions are also given for when the optimal norm is achievable by a controller that regulates robustly. In all cases, controllers are exhibited by giving explicit state-space realizations that carry out the task