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Frequency-Domain Analysis of Linear Time-Periodic Systems

Sandberg, Henrik LU ; Möllerstedt, Erik and Bernhardsson, Bo LU (2004) In Proceedings of the 2004 American Control Conference. 4. p.3357-3362
Abstract
In this paper we study how a system with a time-periodic impulse response may be expanded into a sum of modulated time-invariant systems. This allows us to define a linear frequency-response operator for periodic systems, called the harmonic transfer function (HTF). Similar frequency-response operators have been derived before for sampled-data systems and periodic finite-dimensional state-space systems. The HTF is an infinite-dimensional operator that captures the frequency coupling of a time-periodic system. The paper includes analysis of convergence of truncated HTFs. For this reason the concepts of input/output roll-off are developed and related to time-varying Markov parameters.
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
state-space methods, sampled data systems, periodic control, multidimensional systems, linear systems, harmonic analysis, frequency-domain analysis, frequency response, Markov processes, convergence, time-varying systems, transient response, transfer functions
in
Proceedings of the 2004 American Control Conference.
volume
4
pages
3357 - 3362
publisher
Boston, Massachusetts
external identifiers
  • wos:000224688300570
  • scopus:8744231805
ISSN
0743-1619
ISBN
0-7803-8335-4
language
English
LU publication?
yes
id
96b43cee-30d2-48d7-abb1-ddd249219c87 (old id 536045)
alternative location
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1384427
date added to LUP
2007-09-25 09:55:02
date last changed
2017-01-01 07:00:08
@inproceedings{96b43cee-30d2-48d7-abb1-ddd249219c87,
  abstract     = {In this paper we study how a system with a time-periodic impulse response may be expanded into a sum of modulated time-invariant systems. This allows us to define a linear frequency-response operator for periodic systems, called the harmonic transfer function (HTF). Similar frequency-response operators have been derived before for sampled-data systems and periodic finite-dimensional state-space systems. The HTF is an infinite-dimensional operator that captures the frequency coupling of a time-periodic system. The paper includes analysis of convergence of truncated HTFs. For this reason the concepts of input/output roll-off are developed and related to time-varying Markov parameters.},
  author       = {Sandberg, Henrik and Möllerstedt, Erik and Bernhardsson, Bo},
  booktitle    = {Proceedings of the 2004 American Control Conference.},
  isbn         = {0-7803-8335-4},
  issn         = {0743-1619},
  keyword      = {state-space methods,sampled data systems,periodic control,multidimensional systems,linear systems,harmonic analysis,frequency-domain analysis,frequency response,Markov processes,convergence,time-varying systems,transient response,transfer functions},
  language     = {eng},
  pages        = {3357--3362},
  publisher    = {Boston, Massachusetts},
  title        = {Frequency-Domain Analysis of Linear Time-Periodic Systems},
  volume       = {4},
  year         = {2004},
}