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A Bode sensitivity integral for linear time-periodic systems

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Author

Summary, in English

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.

Publishing year

2004

Language

English

Pages

2644-2649

Publication/Series

Proceedings 43rd IEEE Conference on Decision and Control

Volume

3

Document type

Conference paper

Publisher

IEEE - Institute of Electrical and Electronics Engineers Inc.

Topic

  • Control Engineering

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

Conference name

Reglermöte 2004

Conference date

2004-05-26

Conference place

Göteborg, Sweden

Status

Published

ISBN/ISSN/Other

  • ISSN: 0191-2216
  • ISBN: 0-7803-8682-5