• Let G(s) be any proper real rational transfer matrix, then there
exist unimodular matrices U(s), V(s) Î R[s] such that
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•
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and ai(s)
divides ai+1(s) and bi+1(s) divides bi(s).
•Write G(s) as G(s) = N(s)/d(s) such that d(s) is a scalar polynomial
and N(s) is a p×m polynomial matrix.
Let the Smith form
of N(s) be S(s) = U(s)N(s)V(s).
Then M(s) = S(s)/d(s).