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## 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



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

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