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H-Infinity Control with Nearly Symmetric State Matrix

Vladu, Emil LU orcid and Rantzer, Anders LU orcid (2022) In IEEE Control Systems Letters 6. p.3026-3031
Abstract

In this letter, we give an upper bound on the deviation from H-infinity optimality of a class of controllers as a function of the deviation from symmetry in the state matrix. We further suggest a scalar measure of symmetry which is shown to be directly relevant for estimating nearness to optimality. In connection to this, we give a simple analytical solution to a class of Lyapunov equations for two dimensional state matrices. Finally, we demonstrate how a well-chosen symmetric part for nearly symmetric state matrices may lead not only to near-optimality, but also to controller sparsity, a desirable property for large-scale systems. In the special case that the state matrix is symmetric and Hurwitz, our main result simplifies to give an... (More)

In this letter, we give an upper bound on the deviation from H-infinity optimality of a class of controllers as a function of the deviation from symmetry in the state matrix. We further suggest a scalar measure of symmetry which is shown to be directly relevant for estimating nearness to optimality. In connection to this, we give a simple analytical solution to a class of Lyapunov equations for two dimensional state matrices. Finally, we demonstrate how a well-chosen symmetric part for nearly symmetric state matrices may lead not only to near-optimality, but also to controller sparsity, a desirable property for large-scale systems. In the special case that the state matrix is symmetric and Hurwitz, our main result simplifies to give an H-infinity optimal controller with several benefits, a result which has recently appeared in the literature. In this sense, the above is a significant generalization which considers a much wider class of systems, yet allows one to retain the benefits of symmetric state matrices, while offering means of quantifying the effect of this on the H-infinity norm.

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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
distributed control, large-scale systems, Robust control
in
IEEE Control Systems Letters
volume
6
pages
6 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85131760277
ISSN
2475-1456
DOI
10.1109/LCSYS.2022.3180413
language
English
LU publication?
yes
id
bbb38ead-4cb4-473c-a587-ee3046a3996a
date added to LUP
2022-08-30 14:48:41
date last changed
2023-11-21 10:38:34
@article{bbb38ead-4cb4-473c-a587-ee3046a3996a,
  abstract     = {{<p>In this letter, we give an upper bound on the deviation from H-infinity optimality of a class of controllers as a function of the deviation from symmetry in the state matrix. We further suggest a scalar measure of symmetry which is shown to be directly relevant for estimating nearness to optimality. In connection to this, we give a simple analytical solution to a class of Lyapunov equations for two dimensional state matrices. Finally, we demonstrate how a well-chosen symmetric part for nearly symmetric state matrices may lead not only to near-optimality, but also to controller sparsity, a desirable property for large-scale systems. In the special case that the state matrix is symmetric and Hurwitz, our main result simplifies to give an H-infinity optimal controller with several benefits, a result which has recently appeared in the literature. In this sense, the above is a significant generalization which considers a much wider class of systems, yet allows one to retain the benefits of symmetric state matrices, while offering means of quantifying the effect of this on the H-infinity norm.</p>}},
  author       = {{Vladu, Emil and Rantzer, Anders}},
  issn         = {{2475-1456}},
  keywords     = {{distributed control; large-scale systems; Robust control}},
  language     = {{eng}},
  pages        = {{3026--3031}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Control Systems Letters}},
  title        = {{H-Infinity Control with Nearly Symmetric State Matrix}},
  url          = {{http://dx.doi.org/10.1109/LCSYS.2022.3180413}},
  doi          = {{10.1109/LCSYS.2022.3180413}},
  volume       = {{6}},
  year         = {{2022}},
}