Subspace-based methods for the identification of linear time-invariant systems
type: Item
instance of: scholarly article
title: Subspace-based methods for the identification of linear time-invariant systems
zbMATH Open document ID: 0846.93023
DOI: 10.1016/0005-1098(95)00107-5
author: Mats Viberg
published in: Automatica
publication date: 1996-09-22T00:00:00Z
review text: This tutorial paper explains various subspace-based methods for the identification of linear time-invariant systems. Realization based methods compute the singular value decomposition of the Hankel matrix of the system and the observability and controllability matrices are obtained from this decomposition. They lead, following the known method of Ho and Kalman, to the system matrices. The idea of the direct method consists in projecting the column vectors of a matrix of output data on a space whose range coincides with the range of the observability matrix of a realization of the system. The observability matrix is taken as the matrix left singular vectors of the projected quantity. The system matrices defining the observability matrix are deduced. The other system matrices appear linearly in the overdetermined input-output equation and can be obtained from this equation. When there is noise in the input-output equation, the author shows how instrumental variable methods allow to eliminate their effect in the procedure. In this context, \(Q- R\) methods allow to obtain a complete stochastic realization but the details are not given. A simulation shows that these methods perform comparably to the prediction error method when the input is white but not as well when the input is not rich enough. In formula (25), the presence of noise is not justified since the corresponding section handles the deterministic case.
Mathematics Subject Classification ID: 93B30
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 93-02
zbMATH DE Number: 867791
zbMATH Keywords: subspace-based methods
zbMATH Keywords: identification
zbMATH Keywords: linear
zbMATH Keywords: instrumental variable methods
Wikidata QID: Q59602663
reviewed by: A. Akutowicz
describes a project that uses: System Identification Toolbox
MaRDI profile type: Publication
full work available at URL: 0005-1098(95)00107-5
OpenAlex ID: W2167933592
cites work: A new look at the statistical model identification
cites work: Q3796553
cites work: Fast recursive identification of state space models via exploitation of displacement structure
cites work: All optimal Hankel-norm approximations of linear multivariable systems and theirL,∞-error bounds†
cites work: An Analysis of the Total Least Squares Problem
cites work: Q3359644
cites work: On the Identification of Linear Time-Invariant Systems from Input-Output Data
cites work: Q5521815
cites work: An eigensystem realization algorithm for modal parameter identification and model reduction
cites work: Fast projection methods for minimal design problems in linear system theory
cites work: A generalized approach to q-Markov covariance equivalent realizations for discrete systems
cites work: Q4724470
cites work: Discussion: `On the use of minimal parametrisations in multivariable ARMAX identification' by R. P. Guidorzi
cites work: Comments on 'State-space model identification with data correlation’
cites work: On- and off-line identification of linear state-space models
cites work: QSVD approach to on- and off-line state-space identification
cites work: Analysis of subspace fitting and ML techniques for parameter estimation from sensor array data
cites work: Q4775345
cites work: On covariance function tests used in system identification
cites work: MUSIC, maximum likelihood, and Cramer-Rao bound
cites work: Maximum likelihood methods for direction-of-arrival estimation
cites work: Weighted LS and TLS approaches yield asymptotically equivalent results
cites work: An indirect method for transfer function estimation from closed loop data
cites work: On line structure selection for multivariable state-space models
cites work: Subspace algorithms for the stochastic identification problem
cites work: 4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems
cites work: Application of a subspace model identification technique to identify LTI systems operating in closed-loop
cites work: Subspace model identification Part 3. Analysis of the ordinary output-error state-space model identification algorithm
cites work: Identification of the deterministic part of MIMO state space models given in innovations form from input-output data
cites work: Subspace model identification Part 1. The output-error state-space model identification class of algorithms
cites work: Sensor array processing based on subspace fitting
cites work: Design variables for bias distribution in transfer function estimation
cites work: From time series to linear system. I: Finite dimensional linear time invariant systems
cites work: Approximate linear realizations of given dimension via Ho's algorithm
DBLP publication ID: journals/automatica/Viberg95
description: scientific article; zbMATH DE number 867791