A Bode sensitivity integral for linear timeperiodic systems
(2004) Reglermöte 2004 In Proceedings 43rd IEEE Conference on Decision and Control 3. p.26442649 Abstract
 For linear timeinvariant systems Bode's sensitivity integral is a wellknown formula that quantifies some of thelimitations in feedback control. In this paper we show that a very similar formula holds for linear timeperiodicsystems. We use the infinitedimensional frequencyresponse 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 rolloff 2. A periodic system has rolloff 2 if the first timevarying Markov parameter is equal to zero.
Please use this url to cite or link to this publication:
http://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, timevarying systems, transfer functions, infinitedimensional frequencyresponse operator, harmonic transfer function, Bode sensitivity integral, analytic operator, timevarying Markov parameter, linear timeperiodic systems, frequency response
 in
 Proceedings 43rd IEEE Conference on Decision and Control
 volume
 3
 pages
 2644  2649
 publisher
 IEEEInstitute of Electrical and Electronics Engineers Inc.
 conference name
 Reglermöte 2004
 external identifiers

 wos:000226745602065
 scopus:14244254213
 ISSN
 01912216
 ISBN
 0780386825
 language
 English
 LU publication?
 yes
 id
 7f8134f561f1485284d97909012fa2c1 (old id 536078)
 alternative location
 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1428859
 date added to LUP
 20070925 09:56:30
 date last changed
 20180107 09:45:23
@inproceedings{7f8134f561f1485284d97909012fa2c1, abstract = {For linear timeinvariant systems Bode's sensitivity integral is a wellknown formula that quantifies some of thelimitations in feedback control. In this paper we show that a very similar formula holds for linear timeperiodicsystems. We use the infinitedimensional frequencyresponse 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 rolloff 2. A periodic system has rolloff 2 if the first timevarying Markov parameter is equal to zero.}, author = {Sandberg, Henrik and Bernhardsson, Bo}, booktitle = {Proceedings 43rd IEEE Conference on Decision and Control}, isbn = {0780386825}, issn = {01912216}, keyword = {trace class operator,linear systems,timevarying systems,transfer functions,infinitedimensional frequencyresponse operator,harmonic transfer function,Bode sensitivity integral,analytic operator,timevarying Markov parameter,linear timeperiodic systems,frequency response}, language = {eng}, pages = {26442649}, publisher = {IEEEInstitute of Electrical and Electronics Engineers Inc.}, title = {A Bode sensitivity integral for linear timeperiodic systems}, volume = {3}, year = {2004}, }