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 that there is a continuously parameterized family F of n-dimensional single-input single-output (SISO) stabilizable detectable linear system Sigma (p) which contains at least one realization of each reduced, strictly proper transfer function of McMillan degree not exceeding n. The parameterization map p to Sigma (p) 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.