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Balance Truncation for Discrete Time Markov Jump Linear Systems

Kotsalis, Georgios and Rantzer, Anders LU (2009) In Technical Reports TFRT-7621
Abstract
This paper investigates the model reduction problem for mean square stable discrete time Markov jump linear systems. For this class of systems a balanced truncation algorithm is developed. The reduced order model is suboptimal, however the approximation error, which is captured by means of the stochastic L2 gain, is bounded from above by twice the sum of singular numbers associated to the truncated states of each mode. Such a result allows rigorous simplification of the dynamics of each mode in an independent manner with respect to a metric which is relevant from a robust control point of view.
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Book/Report
publication status
published
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in
Technical Reports TFRT-7621
publisher
Department of Automatic Control, Lund Institute of Technology, Lund University
ISSN
0280-5316
language
English
LU publication?
yes
id
03405fa9-5bca-4deb-a7ee-9667415be2d7 (old id 8602580)
date added to LUP
2016-04-01 14:52:39
date last changed
2018-11-21 20:31:02
@techreport{03405fa9-5bca-4deb-a7ee-9667415be2d7,
  abstract     = {This paper investigates the model reduction problem for mean square stable discrete time Markov jump linear systems. For this class of systems a balanced truncation algorithm is developed. The reduced order model is suboptimal, however the approximation error, which is captured by means of the stochastic L2 gain, is bounded from above by twice the sum of singular numbers associated to the truncated states of each mode. Such a result allows rigorous simplification of the dynamics of each mode in an independent manner with respect to a metric which is relevant from a robust control point of view.},
  author       = {Kotsalis, Georgios and Rantzer, Anders},
  institution  = {Department of Automatic Control, Lund Institute of Technology, Lund University},
  issn         = {0280-5316},
  language     = {eng},
  series       = {Technical Reports TFRT-7621},
  title        = {Balance Truncation for Discrete Time Markov Jump Linear Systems},
  url          = {https://lup.lub.lu.se/search/files/4209906/8627226.pdf},
  year         = {2009},
}