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New Convergence Results for Least Squares Identification Algorithm
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2009 (English)Report (Other academic)
Abstract [en]

The basic least squares method for identifying linear systems has been extensively studied. Conditions for convergence involve issues about noise assumptions and behavior of the sample covariance matrix of the regressors. Lai and Wei proved in 1982 convergence for essentially minimal conditions on the regression matrix: All eigenvalues must tend to infinity, and the logarithm of the largest eigenvalue must not tend to infinity faster than the smallest eigenvalue. In this contribution we revisit this classical result with respect to assumptions on the noise: How much unstructured disturbances can be allowed without affecting the convergence? The answer is that the norm of these disturbances must tend to infinity slower than the smallest eigenvalue of the regression matrix.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2009. , 9 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2904
Keyword [en]
System identification
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-56065ISRN: LiTH-ISY-R-2904OAI: oai:DiVA.org:liu-56065DiVA: diva2:316873
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-08-12Bibliographically approved

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Ljung, Lennart

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf