Frequency-Domain Analysis of Linear Time-Periodic Systems
(2003) In IML-R--29-02/03--SE+spring- Abstract
- In this report we study how a time-varying system with a time-periodic integral kernel (impulse response), g(t,\tau)=g(t+T,\tau+T), can be expanded into a sum of essentially time-invariant systems. This allows us to define a linear frequency response operator for periodic systems, called the Harmonic Transfer Function (HTF). The HTF is a direct analog of the transfer function for time-invariant systems, but it captures the frequency coupling of a time-periodic system. It can, for example, be used to compute the induced L_2-norm of periodic systems. The report also includes analysis of convergence of truncated HTFs, which is essential for practical computations as the HTF is an infinite-dimensional operator.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8602645
- author
- Sandberg, Henrik LU
- organization
- publishing date
- 2003
- type
- Book/Report
- publication status
- published
- subject
- in
- IML-R--29-02/03--SE+spring
- publisher
- Institut Mittag-Leffler, The Swedish Royal Academy of Sciences
- report number
- 32, 2002/2003
- ISSN
- 1103-467X
- language
- English
- LU publication?
- yes
- id
- e9a14ceb-c009-4316-b5fd-da48c8b97ffb (old id 8602645)
- date added to LUP
- 2016-04-01 16:09:08
- date last changed
- 2018-11-21 20:39:09
@techreport{e9a14ceb-c009-4316-b5fd-da48c8b97ffb, abstract = {{In this report we study how a time-varying system with a time-periodic integral kernel (impulse response), g(t,\tau)=g(t+T,\tau+T), can be expanded into a sum of essentially time-invariant systems. This allows us to define a linear frequency response operator for periodic systems, called the Harmonic Transfer Function (HTF). The HTF is a direct analog of the transfer function for time-invariant systems, but it captures the frequency coupling of a time-periodic system. It can, for example, be used to compute the induced L_2-norm of periodic systems. The report also includes analysis of convergence of truncated HTFs, which is essential for practical computations as the HTF is an infinite-dimensional operator.}}, author = {{Sandberg, Henrik}}, institution = {{Institut Mittag-Leffler, The Swedish Royal Academy of Sciences}}, issn = {{1103-467X}}, language = {{eng}}, number = {{32, 2002/2003}}, series = {{IML-R--29-02/03--SE+spring}}, title = {{Frequency-Domain Analysis of Linear Time-Periodic Systems}}, year = {{2003}}, }