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A Bode sensitivity integral for linear time-periodic systems

Sandberg, Henrik LU and Bernhardsson, Bo LU (2004) Reglermöte 2004 In Proceedings 43rd IEEE Conference on Decision and Control 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
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
in
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
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
2007-09-25 09:56:30
date last changed
2017-06-04 04:28:57
@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},
  keyword      = {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},
  volume       = {3},
  year         = {2004},
}