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Balanced truncation of linear time-varying systems

Sandberg, Henrik LU and Rantzer, Anders LU (2004) In IEEE Transactions on Automatic Control 49(2). p.217-229
Abstract
In this paper balanced truncation of linear time-varying systems is studied in discrete and continuous time. Based on relatively basic calculations with time-varying Lyapunov equations/inequalities we are able to derive both upper and lower error bounds for the truncated models. These results generalize well-known time-invariant formulas. The case oftime-varying state dimension is considered. Input-output stability of all truncated balanced realizations is also proven. The method is finally successfully applied to a high-order model.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
linear timevarying systems, Balanced truncation, error bound, model reduction
in
IEEE Transactions on Automatic Control
volume
49
issue
2
pages
217 - 229
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000189037200005
  • scopus:1442264260
ISSN
0018-9286
DOI
10.1109/TAC.2003.822862
language
English
LU publication?
yes
id
8218881a-f521-492b-8de5-c267a09a9f51 (old id 161419)
date added to LUP
2007-07-04 15:47:28
date last changed
2017-12-10 04:37:30
@article{8218881a-f521-492b-8de5-c267a09a9f51,
  abstract     = {In this paper balanced truncation of linear time-varying systems is studied in discrete and continuous time. Based on relatively basic calculations with time-varying Lyapunov equations/inequalities we are able to derive both upper and lower error bounds for the truncated models. These results generalize well-known time-invariant formulas. The case oftime-varying state dimension is considered. Input-output stability of all truncated balanced realizations is also proven. The method is finally successfully applied to a high-order model.},
  author       = {Sandberg, Henrik and Rantzer, Anders},
  issn         = {0018-9286},
  keyword      = {linear timevarying
systems,Balanced truncation,error bound,model reduction},
  language     = {eng},
  number       = {2},
  pages        = {217--229},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Automatic Control},
  title        = {Balanced truncation of linear time-varying systems},
  url          = {http://dx.doi.org/10.1109/TAC.2003.822862},
  volume       = {49},
  year         = {2004},
}