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Covariance Analysis, Positivity and the Yakubovich-Kalman-Popov Lemma

Johansson, Rolf LU and Robertsson, Anders LU (2000) In Proceedings of the 39th IEEE Conference on Decision and Control, 2000. 4. p.3363-3368
Abstract
This paper presents theory and algorithms for covariance analysis and stochastic realization without any minimality condition imposed. Also without any minimality conditions, we show that several properties of covariance factorization and positive realness hold. The results are significant for validation in system identification of state-space models from finite input-output sequences. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem. The case considered includes the problem of... (More)
This paper presents theory and algorithms for covariance analysis and stochastic realization without any minimality condition imposed. Also without any minimality conditions, we show that several properties of covariance factorization and positive realness hold. The results are significant for validation in system identification of state-space models from finite input-output sequences. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem. The case considered includes the problem of rank-deficient residual covariance matrices, a case which is encountered in applications with mixed stochastic-deterministic input-output properties as well as for cases where outputs are linearly dependent,thus extending previous results in covariance analysis. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
state-space methods, identification, covariance analysis, Popov criterion, Riccati equations
in
Proceedings of the 39th IEEE Conference on Decision and Control, 2000.
volume
4
pages
3363 - 3368
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:0034440319
ISBN
0-7803-6638-7
DOI
10.1109/CDC.2000.912222
language
English
LU publication?
yes
id
e1ac421f-6b0c-427f-9773-e6038f8e1346 (old id 538060)
date added to LUP
2007-09-20 16:29:54
date last changed
2017-01-01 07:55:13
@inproceedings{e1ac421f-6b0c-427f-9773-e6038f8e1346,
  abstract     = {This paper presents theory and algorithms for covariance analysis and stochastic realization without any minimality condition imposed. Also without any minimality conditions, we show that several properties of covariance factorization and positive realness hold. The results are significant for validation in system identification of state-space models from finite input-output sequences. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem. The case considered includes the problem of rank-deficient residual covariance matrices, a case which is encountered in applications with mixed stochastic-deterministic input-output properties as well as for cases where outputs are linearly dependent,thus extending previous results in covariance analysis.},
  author       = {Johansson, Rolf and Robertsson, Anders},
  booktitle    = {Proceedings of the 39th IEEE Conference on Decision and Control, 2000.},
  isbn         = {0-7803-6638-7},
  keyword      = {state-space methods,identification,covariance analysis,Popov criterion,Riccati equations},
  language     = {eng},
  pages        = {3363--3368},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  title        = {Covariance Analysis, Positivity and the Yakubovich-Kalman-Popov Lemma},
  url          = {http://dx.doi.org/10.1109/CDC.2000.912222},
  volume       = {4},
  year         = {2000},
}