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A Bode Sensitivity Integral for Linear Time-Periodic Systems

Sandberg, Henrik LU and Bernhardsson, Bo LU orcid (2005) In IEEE Transactions on Automatic Control 50(12). p.2034-2039
Abstract
Bode's sensitivity integral is a well-known formula that quantifies some of the limitations in feedback control for linear time-invariant systems. In this note, we show that there is a similar formula for linear time-periodic systems. The harmonic transfer function is used to prove the result. We use the notion of roll-off 2, which means that the first time-varying Markov parameter is equal to zero. It then follows that the harmonic transfer function is an analytic operator and a trace class operator. These facts are used to prove the result.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Bode sensitivity integral, linear time-periodic systems, performance limitations
in
IEEE Transactions on Automatic Control
volume
50
issue
12
pages
2034 - 2039
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000234062800010
  • scopus:30344454665
ISSN
0018-9286
DOI
10.1109/TAC.2005.860247
language
English
LU publication?
yes
id
c8577d61-dfa7-4cae-a7ea-2e48332cfb54 (old id 160762)
date added to LUP
2016-04-01 15:49:42
date last changed
2022-01-28 07:22:23
@article{c8577d61-dfa7-4cae-a7ea-2e48332cfb54,
  abstract     = {{Bode's sensitivity integral is a well-known formula that quantifies some of the limitations in feedback control for linear time-invariant systems. In this note, we show that there is a similar formula for linear time-periodic systems. The harmonic transfer function is used to prove the result. We use the notion of roll-off 2, which means that the first time-varying Markov parameter is equal to zero. It then follows that the harmonic transfer function is an analytic operator and a trace class operator. These facts are used to prove the result.}},
  author       = {{Sandberg, Henrik and Bernhardsson, Bo}},
  issn         = {{0018-9286}},
  keywords     = {{Bode sensitivity integral; linear time-periodic systems; performance limitations}},
  language     = {{eng}},
  number       = {{12}},
  pages        = {{2034--2039}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Automatic Control}},
  title        = {{A Bode Sensitivity Integral for Linear Time-Periodic Systems}},
  url          = {{https://lup.lub.lu.se/search/files/4484555/625568.pdf}},
  doi          = {{10.1109/TAC.2005.860247}},
  volume       = {{50}},
  year         = {{2005}},
}