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Error Bounds for Balanced Truncation of Linear Time-Varying Systems

Sandberg, Henrik LU and Rantzer, Anders LU orcid (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:
author
and
organization
publishing date
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}},
}