On finite and infinite zeros in the model matching problem

In the model matching problem, proper plant P and model T are given and a proper M is to be found such that T = PM. M can then be realized via feedback and feedforward compensation. For internal stability T and M must be stable. A proper and stable solution M exists only when the unstable finite and infinite zeros of P also appear in T. This is studied using the interactor and the Hermite forms of P and T, directly using factorizations of the transfer matrices and by utilizing and extending results of the related nominal synthesis problem. How to choose an appropriate T in control design is also discussed using polynomial matrix interpolation.