Identification of Nonprime Systems

If a system is exactly described by an irreducible transfer function of unknown degree n and an attempt is made to identify its parameters recursively using an estimate ñ ≫ n for the degree, the actual system poles and zeros will indeed be identified; however, so will ñ - n cancelling poles and zeros. These spurious poles and zeros will tend to jump at random about the z-plane, resulting in wildly varying parameters and giving the impression that convergence has not occurred. We give a method for extracting the parameters of the minimal transfer function from the identified parameters which does not depend on polynomial factorizations, but only on differencing successive estimates. Our approach also determines the degree n of the minimal system description.