A new interpretation of subspace methods by using Schur complement

Author

Takei, Yoshinori ; Imai, Jun ; Wada, Kiyoshi

Author_Institution

Dept. of Electr. & Electron. Eng., Kyushu Univ., Fukuoka, Japan

Volume

4

fYear

2001

fDate

2001

Firstpage

3924

Abstract

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 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 the fact that the Schur complement yielded by the subspace extraction coincides with the error covariance in the least squares, our interpretation paves the way for the derivation of the recursive algorithm of the 4SID method

Keywords

MIMO systems; discrete time systems; identification; least squares approximations; linear systems; matrix algebra; observability; state-space methods; MIMO systems; Schur complement matrix; discrete time systems; error covariance; least squares; linear time-invariant systems; observability; state-space model; subspace methods; Covariance matrix; Data mining; Equations; Instruments; Least squares methods; MIMO; Observability; State estimation; State-space methods; Systems engineering and theory;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2001. Proceedings of the 40th IEEE Conference on

Conference_Location

Orlando, FL

Print_ISBN

0-7803-7061-9

Type

conf

DOI

10.1109/.2001.980489

Filename

980489