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Duality in Robust Control: Controller vs. Uncertainty

Ghulchak, Andrey LU (2001) Conference on Decision and Control 2. p.1113-1118
Abstract
To find a controller that provides the maximal stability margin to an LTI system under rank-one perturbations is a quasiconvex problem. In the paper, the dual quasiconvex problem is obtained, using the convex duality arguments in the Hardy space H∞. It is shown that the dual problem can be viewed as minimization of a "length" of uncertainties that destabilize the system. Several examples establishing a connection with such classical results as the corona theorem and the Adamyan-Arov-Krein theorem are considered
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
uncertain systems, robust control, duality (mathematics), linear systems, minimisation, optimisation
host publication
Proceedings of the 40th IEEE Conference on Decision and Control, 2001.
volume
2
pages
1113 - 1118
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
Conference on Decision and Control
conference location
Orlando, United States
conference dates
2001-12-04
ISBN
0-7803-7061-9
DOI
10.1109/.2001.981034
language
English
LU publication?
yes
id
f1995ede-2ffa-44a8-9455-bd8e02ebfd36 (old id 537880)
date added to LUP
2016-04-04 09:57:03
date last changed
2018-11-21 20:55:49
@inproceedings{f1995ede-2ffa-44a8-9455-bd8e02ebfd36,
  abstract     = {To find a controller that provides the maximal stability margin to an LTI system under rank-one perturbations is a quasiconvex problem. In the paper, the dual quasiconvex problem is obtained, using the convex duality arguments in the Hardy space H∞. It is shown that the dual problem can be viewed as minimization of a "length" of uncertainties that destabilize the system. Several examples establishing a connection with such classical results as the corona theorem and the Adamyan-Arov-Krein theorem are considered},
  author       = {Ghulchak, Andrey},
  booktitle    = {Proceedings of the 40th IEEE Conference on Decision and Control, 2001.},
  isbn         = {0-7803-7061-9},
  language     = {eng},
  pages        = {1113--1118},
  publisher    = {IEEE - Institute of Electrical and Electronics Engineers Inc.},
  title        = {Duality in Robust Control: Controller vs. Uncertainty},
  url          = {https://lup.lub.lu.se/search/ws/files/5424358/625717.pdf},
  doi          = {10.1109/.2001.981034},
  volume       = {2},
  year         = {2001},
}