Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

A Bode sensitivity integral for linear time-periodic systems

Sandberg, Henrik LU and Bernhardsson, Bo LU orcid (2004) Reglermöte 2004 3. p.2644-2649
Abstract
For linear time-invariant systems Bode's sensitivity integral is a well-known formula that quantifies some of thelimitations in feedback control. In this paper we show that a very similar formula holds for linear time-periodicsystems. We use the infinite-dimensional frequency-response operator called the harmonic transfer function to prove the result. It is shown that the harmonic transfer function isan analytic operator and a trace class operator under the assumption that the periodic system has roll-off 2. A periodic system has roll-off 2 if the first time-varying Markov parameter is equal to zero.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
trace class operator, linear systems, time-varying systems, transfer functions, infinite-dimensional frequency-response operator, harmonic transfer function, Bode sensitivity integral, analytic operator, time-varying Markov parameter, linear time-periodic systems, frequency response
host publication
Proceedings 43rd IEEE Conference on Decision and Control
volume
3
pages
2644 - 2649
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
Reglermöte 2004
conference location
Göteborg, Sweden
conference dates
2004-05-26
external identifiers
  • wos:000226745602065
  • scopus:14244254213
ISSN
0191-2216
ISBN
0-7803-8682-5
language
English
LU publication?
yes
id
7f8134f5-61f1-4852-84d9-7909012fa2c1 (old id 536078)
alternative location
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1428859
date added to LUP
2016-04-01 17:06:01
date last changed
2022-01-29 00:22:59
@inproceedings{7f8134f5-61f1-4852-84d9-7909012fa2c1,
  abstract     = {{For linear time-invariant systems Bode's sensitivity integral is a well-known formula that quantifies some of thelimitations in feedback control. In this paper we show that a very similar formula holds for linear time-periodicsystems. We use the infinite-dimensional frequency-response operator called the harmonic transfer function to prove the result. It is shown that the harmonic transfer function isan analytic operator and a trace class operator under the assumption that the periodic system has roll-off 2. A periodic system has roll-off 2 if the first time-varying Markov parameter is equal to zero.}},
  author       = {{Sandberg, Henrik and Bernhardsson, Bo}},
  booktitle    = {{Proceedings 43rd IEEE Conference on Decision and Control}},
  isbn         = {{0-7803-8682-5}},
  issn         = {{0191-2216}},
  keywords     = {{trace class operator; linear systems; time-varying systems; transfer functions; infinite-dimensional frequency-response operator; harmonic transfer function; Bode sensitivity integral; analytic operator; time-varying Markov parameter; linear time-periodic systems; frequency response}},
  language     = {{eng}},
  pages        = {{2644--2649}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{A Bode sensitivity integral for linear time-periodic systems}},
  url          = {{https://lup.lub.lu.se/search/files/4874578/625613.pdf}},
  volume       = {{3}},
  year         = {{2004}},
}