Frequency-Domain Analysis of Linear Time-Periodic Systems
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/160757
- author
- Sandberg, Henrik LU ; Möllerstedt, Erik and Bernhardsson, Bo LU
- organization
- publishing date
- 2005
- 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
- 2016-04-01 16:56:03
- date last changed
- 2022-03-22 22:13:12
@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}}, keywords = {{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 = {{https://lup.lub.lu.se/search/files/4822918/625567.pdf}}, doi = {{10.1109/TAC.2005.860294}}, volume = {{50}}, year = {{2005}}, }