Generalized Bezoutian and Sylvester matrices in multivariable linear control

Generalized Bezoutian and Sylvester matrices are defined and discussed in this short paper. The relationship between these two forms of matrices is established. It is shown that the McMillan degree of a real rational function can be ascertained by checking the rank of either one of these generalized matrices formed using a polynomial matrix fraction decomposition of the prescribed transfer function matrix. Earlier established results by Rowe and Munro are obtained as a special case. Several theorems related to the rank testing and other properties of the generalized matrices are discussed and various research problems are listed in the conclusion.