QSVD approach to on- and off-line state-space identification

Abstract

Moonen et al. (1989 a), presented an SVD-based identification scheme for computing state-space models for multivariable linear time-invariant systems. In the present paper, this identification procedure is reformulated making use of the quotient singular value decomposition (QSVD). Here the input-output error co-variance matrix can be taken into account explicitly, thus extending the applicability of the identification scheme to the case were the input and output data are corrupted by coloured noise. It turns out that in practice, due to the use of various pre-filtering techniques (anti-aliasing, etc.), this latter case is most often encountered. The extended identification scheme explicitly compensates for the filter characteristics and the consistency of the identification results follows from the consistency results for the QSVD. The usefulness of this generalization is demonstrated. The development is largely inspired by recent progress in total least-squares solution techniques (Van Huffel 1989) for the identification of static linear relations. The present identification scheme can therefore be viewed as the analogous counterpart for identifying dynamic linear relations.