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Frequency-Domain Analysis of Linear Time-Periodic Systems

Sandberg, Henrik LU ; Möllerstedt, Erik and Bernhardsson, Bo LU orcid (2004) 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.
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
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
host publication
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
2016-04-01 16:15:15
date last changed
2022-01-28 18:23:09
@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}},
  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}},
  language     = {{eng}},
  pages        = {{3357--3362}},
  publisher    = {{Boston, Massachusetts}},
  title        = {{Frequency-Domain Analysis of Linear Time-Periodic Systems}},
  url          = {{http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1384427}},
  volume       = {{4}},
  year         = {{2004}},
}