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A Bode Sensitivity Integral for Linear Time-Periodic Systems

Sandberg, Henrik LU and Bernhardsson, Bo LU (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.
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author
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
2007-07-04 14:45:12
date last changed
2017-07-30 04:29:55
@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},
  keyword      = {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          = {http://dx.doi.org/10.1109/TAC.2005.860247},
  volume       = {50},
  year         = {2005},
}