Let G(s) be a p×m
transfer matrix G(s) =N(s)/d(s)
with d(s) a scalar polynomial. For simplicity, we shall
assume that d(s) has only real and distinct roots li ¹ lj if i ¹ j and
Then G(s) has the following partial fractional expansion:
Suppose
rank Wi = ki and let
BiÎ Rki×m and Ci Î Rp×ki be two constant matrices such that Wi = CiBi.
Then a realization is given by
This realization is controllable and observable (minimal)
by PBH tests.