Closed-loop subspace identification : an orthogonal projection approach

Biao HUANG*, Steven X. DING, S. Joe QIN

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

164 Citations (Scopus)


In this paper, a closed-loop subspace identification approach through an orthogonal projection and subsequent singular value decomposition is proposed. As a by-product of this development, it explains why some existing subspace methods may deliver a bias in the presence of the feedback control and suggests a remedy to eliminate the bias. Furthermore, as the proposed method is a projection based method, it can simultaneously provide extended observability matrix, lower triangular block-Toeplitz matrix, and Kalman filtered state sequences. Therefore, using this method, the system state space matrices can be recovered either from the extended observability matrix/the block-Toeplitz matrix or from the Kalman filter state sequences. © 2004 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)53-66
Number of pages14
JournalJournal of Process Control
Issue number1
Early online date15 Jun 2004
Publication statusPublished - Feb 2005
Externally publishedYes

Bibliographical note

This work is supported by Alexander von Humboldt Research Fellowship of Germany and this support is greatly acknowledged by B.H. and S.X.D. S.J.Q. also acknowledges the support from Natural Sciences Foundation of China in the form of an Outstanding Young Investigator Award for Overseas (60228001).


  • Closed-loop identification
  • Instrument variable method
  • PCA
  • Projection
  • Singular value decomposition
  • Subspace PCA
  • Subspace identification


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