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

摘要

It is shown constructively that there is a continuously parameterized family F of n-dimensional single-input single-output (SISO), stabilizable, detectable linear systems Sigma (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 R/sup 2n/ to the linear space of all SISO n-dimensional linear systems.