Existence conditions of decoupling controllers in the generalized plant model

Necessary and sufficient conditions for the existence of diagonal, block-diagonal and triangular decoupling controllers in linear multivariable systems are presented for the most general setting. The plant model in this paper is general enough to accommodate non-square plant and non-unity feedback cases with 1DOF (one-degree-of-freedom) or 2DOF controller configuration. It is shown that the existence condition is finally described in terms of rank conditions on coefficient matrices in partial fraction expansion.