A new interpretation of subspace methods by using Schur complement

Yoshinori Takei, Jun Imai, Kiyoshi Wada

Research output: Contribution to journalConference articlepeer-review


In this paper, we present a new interpretation of the subspace-based state space system identification (4SID) method by using a subspace extraction via Schur complement (SES). Several efficient implementations of subspace-based identification methods (e.g., N4SID, etc) have been thus far developed and proposed. We consider the MIMO output error state space model identification, the so-called MOESP. Making a comparison between the matrix obtained by the QR factorization in the MOESP and the Schur complement matrix of data product moments shows that the estimate of the extended observability matrix can be obtained by using the SES procedure. Viewing that fact that the Schur complement yielded by the subspace extraction coincides with the error covariance in the least squares (LS), our interpretation will pave the way for the derivation of the recursive algorithm of the 4SID method.

Original languageEnglish
Pages (from-to)3924-3929
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Publication statusPublished - Dec 1 2001
Externally publishedYes
Event40th IEEE Conference on Decision and Control (CDC) - Orlando, FL, United States
Duration: Dec 4 2001Dec 7 2001

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization


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