A Bode sensitivity integral for linear time-periodic systems

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.

• Författare: Henrik Sandberg; Bo Bernhardsson
• Avdelning/ar: Institutionen för reglerteknik
• Publiceringsår: 2004
• Språk: Engelska
• Sidor: 2644-2649
• Publikation/Tidskrift/Serie: Proceedings 43rd IEEE Conference on Decision and Control
• Volym: 3
• Fulltext: - 168 kB; Download statistics
• Länkar: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1428859
• Dokumenttyp: Konferensbidrag
• Förlag: IEEE - Institute of Electrical and Electronics Engineers Inc.
• Ämne: Control Engineering
• Nyckelord: 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/Övrigt: ISSN: 0191-2216; ISBN: 0-7803-8682-5