A Bode sensitivity integral for linear time-periodic systems
2004 (English)In: 2004 43RD IEEE CONFERENCE ON DECISION AND CONTROL (CDC), VOLS 1-5, 2004, Vol. 3, 2644-2649 p.Conference paper (Refereed)
For linear time-invariant systems Bode’s sensitivity integral is a well-known formula that quantifies some of the limitations in feedback control. In this paper we show that a very similar formula holds for linear time-periodic systems. 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 is an 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.
Place, publisher, year, edition, pages
2004. Vol. 3, 2644-2649 p.
, IEEE CONFERENCE ON DECISION AND CONTROL - PROCEEDINGS, ISSN 0191-2216
Bode sensitivity integral; analytic operator; harmonic transfer function; infinite-dimensional frequency-response operator; linear time-periodic systems; time-varying Markov parameter; trace class operator; frequency response; linear systems; time-varying systems; transfer functions;
IdentifiersURN: urn:nbn:se:kth:diva-74715DOI: 10.1109/CDC.2004.1428859ISI: 000226745602065ISBN: 0-7803-8682-5OAI: oai:DiVA.org:kth-74715DiVA: diva2:489884
43rd IEEE Conference on Decision and Control. San Diego, CA. DEC 14-17, 2004
QC 201202062012-02-032012-02-032012-02-06Bibliographically approved