H 2 design of one-degree-of-freedom decoupling controllers for square plants

Decoupling design of one-degree-of-freedom controllers is treated for the generalised plant model within the H ₂ framework. The class of all realisable closed loop transfer matrices is parametrised under a mild assumption on non-unity feedback sensors. A set of compact assumptions is presented to guarantee the existence of the optimal H ₂ controller. Together with the optimal one, the class of all H ₂ controllers that yield finite H ₂ cost is obtained. The optimal closed transfer matrix and its associated controller are shown to be strictly proper under the reasonable order assumptions on the generalised plant.