The Existence of M and N Matrices in the Generalized Formulation for MIMO QFT

Considered in this paper is the question of for what type of multivariable systems is the generalized formulation effective in conditioning the SISO equivalent plants that are pivotal in MIMO QFT design. It is shown by example that for some plant cases there is no benefit to be gained by using the generalized formulation. However, this does not necessarily suggest that no such M and N matrices exist which give desirable SISO equivalent plants. The Smith-McMillan form is used to derive a result for a general nominal MIMO plant. We show that, for any nominal MIMO plant with no unstable blocking poles there exists a pair of M and N matrices such that the resulting conditioned plant yields stable equivalent SISO plants.