A Generalized Framework of Linear Multivariable Control

7.5 To determine the Smith-McMillan form of a rational matrix

In this section we discuss briefly how the procedures proposed above can be used to find the Smith-McMillan form of a rational matrix. If we can construct a right (left) coprime polynomial MFD from the given rational matrix, then the problem of finding the Smith-McMillan form of a rational matrix is reduced to that of determining the Smith forms of the polynomial matrices via the following known result.

Proposition 7.5.1

[5]

Let $T(s)\in \mathfrak{R}{(s)}^{p\times m}$ with ${\mathrm{rank}}_{\mathfrak{R}(s)}T(s)=r,r\le min\{p,m\}$and let $T$