Balanced parametrizations and canonical forms for system identification

This paper contains a review of recent results concerning the parametrization of asymptotically stable linear systems using balanced realizations. Particular emphasis is given on the application of these results to system identification. This work is part of a continuing programme aimed at elucidating the role of balanced realization in system identification.

Balanced realisations of all-pass systems using exact arithmetic with application to the approximation of delay systems

Numerically well-conditioned state-space realisations for all-pass systems, such as Padé approximations to exp(-s), are derived that can be computed using exact integer arithmetic. This is then applied to the a series of functions of exp(-s). It is also shown that the H-infinity norm of the transfer function from the input to the state of a balanced realisation of the Padé approximation of exp(-s) is unity. © 2012 IEEE.