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Existence of Discrete-Time LQG-Controllers

Hagander, Per LU and Hansson, Anders (1995) In Systems & Control Letters 26(4). p.231-238
Abstract
Existence results for the LQG-controller are investigated. An infimal Riccati equation based controller may potentially give closed loop eigenvalues on the unit circle. Assuming left and right invertibility it is shown that there exists an optimal controller if and only if the Riccati equation based controller stabilizes the closed loop system after removal of all its unobservable and uncontrollable modes. Furthermore this reduced controller is the optimal controller, and its transfer function is unique. This existence condition is a considerable simplification of the more general geometric condition recently derived by Trentelman and Stoorvogel.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Systems & Control Letters
volume
26
issue
4
pages
231 - 238
publisher
Elsevier
external identifiers
  • scopus:0029496330
ISSN
0167-6911
DOI
10.1016/0167-6911(95)00006-U
language
English
LU publication?
yes
id
384e8487-6ec3-4468-8a19-3a47a3d9259c (old id 8496949)
date added to LUP
2015-12-30 13:44:53
date last changed
2019-01-06 12:02:42
@article{384e8487-6ec3-4468-8a19-3a47a3d9259c,
  abstract     = {Existence results for the LQG-controller are investigated. An infimal Riccati equation based controller may potentially give closed loop eigenvalues on the unit circle. Assuming left and right invertibility it is shown that there exists an optimal controller if and only if the Riccati equation based controller stabilizes the closed loop system after removal of all its unobservable and uncontrollable modes. Furthermore this reduced controller is the optimal controller, and its transfer function is unique. This existence condition is a considerable simplification of the more general geometric condition recently derived by Trentelman and Stoorvogel.},
  author       = {Hagander, Per and Hansson, Anders},
  issn         = {0167-6911},
  language     = {eng},
  number       = {4},
  pages        = {231--238},
  publisher    = {Elsevier},
  series       = {Systems & Control Letters},
  title        = {Existence of Discrete-Time LQG-Controllers},
  url          = {http://dx.doi.org/10.1016/0167-6911(95)00006-U},
  volume       = {26},
  year         = {1995},
}