Brief Consistency analysis of subspace identification methods based on a linear regression approach

Authors:
Torben Knudsen
Affiliations:
Aalborg University, Institute of Electronic Systems, Department of Control Engineering, Fredrik Bajers Vej 7C, DK-9220 Aalborg Ø, Denmark
Venue:
Automatica (Journal of IFAC)
Year:
2001

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Abstract

In the literature results can be found which claim consistency for the subspace method under certain quite weak assumptions. Unfortunately, a new result gives a counter example showing inconsistency under these assumptions and then gives new more strict sufficient assumptions which however does not include important model structures such as, e.g. Box-Jenkins. Based on a simple least-squares approach this paper shows the possible inconsistency under the weak assumptions and develops only slightly stricter assumptions sufficient for consistency and which includes any model structure.