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A Bode Sensitivity Integral for Linear Time-Periodic Systems

Publiceringsår: 2005
Språk: Engelska
Sidor: 2034-2039
Publikation/Tidskrift/Serie: IEEE Transactions on Automatic Control
Volym: 50
Nummer: 12
Dokumenttyp: Artikel
Förlag: IEEE Control Systems Society


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.



  • Control Engineering
  • Bode sensitivity integral
  • linear time-periodic systems
  • performance limitations


  • ISSN: 0018-9286

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