Smith-McMillan Form

• Let *G(s)* be any proper real rational transfer matrix, then there
exist unimodular matrices *U(s), V(s) *Î **R**[s] such that

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).*