Decoupling precompensation and optimal decoupling

We study decoupling control under a unity-feedback configuration for linear multivariable plants. We parametrize the set of all admissible decoupling precompensators. With the parametrization, it is shown that decoupling controller design is equivalent to a set of SISO controller designs. The parametrization is also used to establish a necessary and sufficient condition for the existence of a stable decoupling controller. Optimal decoupling controller design is proposed and the cost of decoupling is discussed.