Balanced truncation of linear time-varying systems
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/161419
- author
- Sandberg, Henrik LU and Rantzer, Anders LU
- organization
- publishing date
- 2004
- 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
- 2016-04-01 16:53:54
- date last changed
- 2023-11-14 19:59:07
@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}}, keywords = {{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 = {{https://lup.lub.lu.se/search/files/4812893/625601.pdf}}, doi = {{10.1109/TAC.2003.822862}}, volume = {{49}}, year = {{2004}}, }