Error Bounds for Balanced Truncation of Linear Time-Varying Systems
(2002) 3. p.2892-2897- Abstract
- In this paper error bounds for truncated balanced linear time-varying systems in discrete time are obtained. The analysis is based on direct calculations with the time-varying observability and controllability Lyapunov inequalities. The obtained bounds in the induced l-script -norm generalize well-known error-bound formulas for time-invariant systems. The case of time-varying state-space dimension is considered, and this proves to be valuable both for technical and practical reasons. Input-output stability of truncated models is shown to be guaranteed.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/537692
- author
- Sandberg, Henrik LU and Rantzer, Anders LU
- organization
- publishing date
- 2002
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- controllability, linear systems, state-space methods, stability, reduced order systems, observability, time-varying systems, discrete time systems, Lyapunov methods
- host publication
- Proceedings of the 41st IEEE Conference on Decision and Control, 2002
- volume
- 3
- pages
- 2892 - 2897
- publisher
- Las Vegas, Nevada
- external identifiers
-
- wos:000181352300519
- scopus:0036993711
- ISSN
- 0191-2216
- ISBN
- 0-7803-7516-5
- language
- English
- LU publication?
- yes
- id
- 87706792-1838-49fb-9b82-45b7afdbb68c (old id 537692)
- alternative location
- http://ieeexplore.ieee.org/iel5/8437/26568/01184288.pdf
- date added to LUP
- 2016-04-01 15:48:29
- date last changed
- 2023-09-04 06:59:10
@inproceedings{87706792-1838-49fb-9b82-45b7afdbb68c, abstract = {{In this paper error bounds for truncated balanced linear time-varying systems in discrete time are obtained. The analysis is based on direct calculations with the time-varying observability and controllability Lyapunov inequalities. The obtained bounds in the induced l-script -norm generalize well-known error-bound formulas for time-invariant systems. The case of time-varying state-space dimension is considered, and this proves to be valuable both for technical and practical reasons. Input-output stability of truncated models is shown to be guaranteed.}}, author = {{Sandberg, Henrik and Rantzer, Anders}}, booktitle = {{Proceedings of the 41st IEEE Conference on Decision and Control, 2002}}, isbn = {{0-7803-7516-5}}, issn = {{0191-2216}}, keywords = {{controllability; linear systems; state-space methods; stability; reduced order systems; observability; time-varying systems; discrete time systems; Lyapunov methods}}, language = {{eng}}, pages = {{2892--2897}}, publisher = {{Las Vegas, Nevada}}, title = {{Error Bounds for Balanced Truncation of Linear Time-Varying Systems}}, url = {{https://lup.lub.lu.se/search/files/4478218/625681.pdf}}, volume = {{3}}, year = {{2002}}, }