Dr Chris Guiver C.Guiver@napier.ac.uk
Lecturer
Bounded real and positive real balanced truncation for infinite-dimensional systems
Guiver, Christopher; Opmeer, Mark R.
Authors
Mark R. Opmeer
Abstract
Bounded real balanced truncation for infinite-dimensional systems is considered. This provides reduced order finite-dimensional systems that retain bounded realness. We obtain an error bound analogous to the finite-dimensional case in terms of the bounded real singular values. By using the Cayley transform a gap metric error bound for positive real balanced truncation is subsequently obtained. For a class of systems with an analytic semigroup, we show rapid decay of the bounded real and positive real singular values. Together with the established error bounds, this proves rapid convergence of the bounded real and positive real balanced truncations.
Journal Article Type | Article |
---|---|
Publication Date | 2013-03 |
Deposit Date | Jul 23, 2020 |
Publicly Available Date | Aug 13, 2020 |
Journal | Mathematical Control and Related Fields |
Print ISSN | 2156-8472 |
Publisher | American Institute of Mathematical Sciences |
Peer Reviewed | Peer Reviewed |
Volume | 3 |
Issue | 1 |
Pages | 83-119 |
DOI | https://doi.org/10.3934/mcrf.2013.3.83 |
Keywords | positive real., well-posed linear system, Model reduction, infinite-dimensional system, balanced truncation, bounded real |
Public URL | http://researchrepository.napier.ac.uk/Output/2677379 |
Files
Bounded Real And Positive Real Balanced Truncation For Infinite-dimensional Systems (accepted version)
(531 Kb)
PDF
You might also like
Dynamic observers for unknown populations
(2020)
Journal Article
Semi-global incremental input-to-state stability of discrete-time Lur'e systems
(2020)
Journal Article
A circle criterion for strong integral input-to-state stability
(2019)
Journal Article
Infinite-dimensional Lur'e systems: input-to-state stability and convergence properties
(2019)
Journal Article
Infinite-dimensional Lur'e systems with almost periodic forcing
(2020)
Journal Article
Downloadable Citations
About Edinburgh Napier Research Repository
Administrator e-mail: repository@napier.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search