A Bode sensitivity integral for linear time-periodic systems
(2004) Reglermöte 2004 3. p.2644-2649- Abstract
- For linear time-invariant systems Bode's sensitivity integral is a well-known formula that quantifies some of thelimitations in feedback control. In this paper we show that a very similar formula holds for linear time-periodicsystems. We use the infinite-dimensional frequency-response operator called the harmonic transfer function to prove the result. It is shown that the harmonic transfer function isan analytic operator and a trace class operator under the assumption that the periodic system has roll-off 2. A periodic system has roll-off 2 if the first time-varying Markov parameter is equal to zero.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/536078
- author
- Sandberg, Henrik LU and Bernhardsson, Bo LU
- organization
- publishing date
- 2004
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- trace class operator, linear systems, time-varying systems, transfer functions, infinite-dimensional frequency-response operator, harmonic transfer function, Bode sensitivity integral, analytic operator, time-varying Markov parameter, linear time-periodic systems, frequency response
- host publication
- Proceedings 43rd IEEE Conference on Decision and Control
- volume
- 3
- pages
- 2644 - 2649
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- Reglermöte 2004
- conference location
- Göteborg, Sweden
- conference dates
- 2004-05-26
- external identifiers
-
- wos:000226745602065
- scopus:14244254213
- ISSN
- 0191-2216
- ISBN
- 0-7803-8682-5
- language
- English
- LU publication?
- yes
- id
- 7f8134f5-61f1-4852-84d9-7909012fa2c1 (old id 536078)
- alternative location
- http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1428859
- date added to LUP
- 2016-04-01 17:06:01
- date last changed
- 2022-01-29 00:22:59
@inproceedings{7f8134f5-61f1-4852-84d9-7909012fa2c1, abstract = {{For linear time-invariant systems Bode's sensitivity integral is a well-known formula that quantifies some of thelimitations in feedback control. In this paper we show that a very similar formula holds for linear time-periodicsystems. We use the infinite-dimensional frequency-response operator called the harmonic transfer function to prove the result. It is shown that the harmonic transfer function isan analytic operator and a trace class operator under the assumption that the periodic system has roll-off 2. A periodic system has roll-off 2 if the first time-varying Markov parameter is equal to zero.}}, author = {{Sandberg, Henrik and Bernhardsson, Bo}}, booktitle = {{Proceedings 43rd IEEE Conference on Decision and Control}}, isbn = {{0-7803-8682-5}}, issn = {{0191-2216}}, keywords = {{trace class operator; linear systems; time-varying systems; transfer functions; infinite-dimensional frequency-response operator; harmonic transfer function; Bode sensitivity integral; analytic operator; time-varying Markov parameter; linear time-periodic systems; frequency response}}, language = {{eng}}, pages = {{2644--2649}}, publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}}, title = {{A Bode sensitivity integral for linear time-periodic systems}}, url = {{https://lup.lub.lu.se/search/files/4874578/625613.pdf}}, volume = {{3}}, year = {{2004}}, }