A review of stable exact model matching by state feedback

The problem of exact model matching by static state feedback is revisited. The main approaches applied to solve the problem are reviewed. The original solution based on matrix fraction descriptions is used to obtain a new parametric stable solution to the model matching problem. A constructive procedure is given that is based on column degree control and determinant control of a polynomial matrix. An interpretation of the existence conditions is provided in terms of equivalence relations over the rings of polynomials, proper rational functions, and proper and stable rational functions.