A Bode Sensitivity Integral for Linear Time-Periodic Systems
(2005) In IEEE Transactions on Automatic Control 50(12). p.2034-2039- Abstract
- Bode's sensitivity integral is a well-known formula that quantifies some of the limitations in feedback control for linear time-invariant systems. In this note, we show that there is a similar formula for linear time-periodic systems. The harmonic transfer function is used to prove the result. We use the notion of roll-off 2, which means that the first time-varying Markov parameter is equal to zero. It then follows that the harmonic transfer function is an analytic operator and a trace class operator. These facts are used to prove the result.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/160762
- author
- Sandberg, Henrik LU and Bernhardsson, Bo LU
- organization
- publishing date
- 2005
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Bode sensitivity integral, linear time-periodic systems, performance limitations
- in
- IEEE Transactions on Automatic Control
- volume
- 50
- issue
- 12
- pages
- 2034 - 2039
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- wos:000234062800010
- scopus:30344454665
- ISSN
- 0018-9286
- DOI
- 10.1109/TAC.2005.860247
- language
- English
- LU publication?
- yes
- id
- c8577d61-dfa7-4cae-a7ea-2e48332cfb54 (old id 160762)
- date added to LUP
- 2016-04-01 15:49:42
- date last changed
- 2022-01-28 07:22:23
@article{c8577d61-dfa7-4cae-a7ea-2e48332cfb54, abstract = {{Bode's sensitivity integral is a well-known formula that quantifies some of the limitations in feedback control for linear time-invariant systems. In this note, we show that there is a similar formula for linear time-periodic systems. The harmonic transfer function is used to prove the result. We use the notion of roll-off 2, which means that the first time-varying Markov parameter is equal to zero. It then follows that the harmonic transfer function is an analytic operator and a trace class operator. These facts are used to prove the result.}}, author = {{Sandberg, Henrik and Bernhardsson, Bo}}, issn = {{0018-9286}}, keywords = {{Bode sensitivity integral; linear time-periodic systems; performance limitations}}, language = {{eng}}, number = {{12}}, pages = {{2034--2039}}, publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}}, series = {{IEEE Transactions on Automatic Control}}, title = {{A Bode Sensitivity Integral for Linear Time-Periodic Systems}}, url = {{https://lup.lub.lu.se/search/files/4484555/625568.pdf}}, doi = {{10.1109/TAC.2005.860247}}, volume = {{50}}, year = {{2005}}, }