A smoothly parameterized family of stabilizable, observable linear systems containing realizations of all transfer functions of McMillan degree not exceeding n

It is shown constructively that there is a continuously parameterized family F of n-dimensional single-input single-output (SISO), stabilizable, detectable linear systems Σ( p) which contains at least one realization of each reduced, strictly proper transfer function of McMillan degree not exceeding n . The parameterization map is a polynomial function in 2n indeterminates from an open, convex polyhedron in R²ⁿ to the linear space of all SISO n-dimensional linear systems