Optimal $H_{2}$ design of the one-degree-of-freedom decoupling controllers

In this paper, $H_{2}$ designs for the one-degree-of-freedom decoupling control systems are treated for the generalized plant. The optimal $H_{2}$ controller is obtained together with the ones that yield finite $H_{2}$ cost functions under compact assumptions. It is shown that the optimal closed transfer matrix is strictly proper under the reasonable order assumptions on the generalized plant.