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Error Bounds for Balanced Truncation of Linear Time-Varying Systems

Sandberg, Henrik LU and Rantzer, Anders LU (2002) In Proceedings of the 41st IEEE Conference on Decision and Control, 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.
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author
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
in
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
2007-09-25 09:57:49
date last changed
2017-08-20 04:18:47
@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},
  keyword      = {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},
  volume       = {3},
  year         = {2002},
}