title:	Application of Real Rational Modules in System Identification
authors:	Tzvetan Ivanov, P.-A. Absil, Brian D. O. Anderson, Michel Gevers
abstract:	This paper introduces a real rational module framework in the context of Prediction Error Identification using Box-Jenkins model structures. This module framework, which can easily be extended to other model structures, allows us to solve and/or extend a number of problems related to the computation of error norms that arise in system identification. Our main contribution to system identification is an extension of the asymptotic variance formulas for Box-Jenkins models derived by Ninness and Hjalmarsson to asymptotic auto-covariance with respect to frequency. This is achieved by viewing the sensitivity space of the prediction error as a so-called rational module. The auto-covariance of the transfer function estimates at different frequencies can then be quantified in terms of the poles and zeros of the underlying system and the input spectrum. Another application of our rational module framework is the derivation of bounds for the $H^\infty$-norm by the $H^2$-norm that are tight for finite-dimensional systems.
keywords:	System Identification, Auto-Covariance, Rational Modules.
status:	accepted and presented at CDC08
download:	paper (pdf), slides (pdf), slides with audio (swf)
follow up:	ERNSI talk (html)