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Frequency-Domain Analysis of Linear Time-Periodic Systems

Sandberg, Henrik LU ; Möllerstedt, Erik and Bernhardsson, Bo LU (2005) In IEEE Transactions on Automatic Control 50(12). p.1971-1983
Abstract
In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections... (More)
In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
series expansions, frequency-response operators, Convergence analysis, linear time-periodic systems
in
IEEE Transactions on Automatic Control
volume
50
issue
12
pages
1971 - 1983
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000234062800004
  • scopus:30344466922
ISSN
0018-9286
DOI
10.1109/TAC.2005.860294
language
English
LU publication?
yes
id
01c9c17d-1f84-455d-9a80-37c4c4cc2bd5 (old id 160757)
date added to LUP
2007-07-04 15:51:43
date last changed
2017-11-19 04:13:46
@article{01c9c17d-1f84-455d-9a80-37c4c4cc2bd5,
  abstract     = {In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature.},
  author       = {Sandberg, Henrik and Möllerstedt, Erik and Bernhardsson, Bo},
  issn         = {0018-9286},
  keyword      = {series expansions,frequency-response operators,Convergence analysis,linear time-periodic systems},
  language     = {eng},
  number       = {12},
  pages        = {1971--1983},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Automatic Control},
  title        = {Frequency-Domain Analysis of Linear Time-Periodic Systems},
  url          = {http://dx.doi.org/10.1109/TAC.2005.860294},
  volume       = {50},
  year         = {2005},
}