Optimal regulation for linear non right-invertible plants

In this paper we deal with the output regulation problem for an LTI plant whose controllable outputs are more than the control inputs. For the case of constant references, we present a two-degree-of-freedom control scheme which minimizes a quadratic cost function. This cost function weights the tracking error at steady-state. Our methodology is based on the singular value decomposition of the static gain matrix of the plant. Then we show how, introducing some stronger assumptions, it is possible to modify the controller so as to reduce the steady-state control effort.