ROBUST REGULATION WITH H(2) PERFORMANCE

We consider the problem of minimizing the H-2 norm of a feedback syste m subject to the constraint that the controller robustly regulate agai nst constants and sinusoids. We show that, for any epsilon > 0, there exists a controller that both achieves robust regulation and renders t he closed-loop H2 norm within epsilon of the optimal norm (the norm ac hievable without the robust regulation constraint). We also provide co nditions that are both necessary and sufficient for there to exist a r obustly regulating controller that achieves the optimal H2 norm. All p roofs are constructive.