Use of a Luenberger observer to control the numerator and denominator of a transfer function

It is shown that a Luenberger observer may be used to convert a transfer function having a numerator of degree m and a denominator of degree n (with m¿n¿1) into one having a numerator of degree n+m¿1 and a denominator of degree 2n¿1, with the denominator polynomial and n¿1 of the numerator coefficients assignable arbitrarily.