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A Bode Sensitivity Integral for Linear Time-Periodic Systems

Sandberg, Henrik and Bernhardsson, Bo (2005) A Bode Sensitivity Integral for Linear Time-Periodic Systems. IEEE Transactions on Automatic Control, 50 (12). pp. 2034-2039. ISSN 0018-9286. doi:10.1109/TAC.2005.860247.

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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.

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Additional Information:© Copyright 2005 IEEE. "Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.” Manuscript received November 4, 2004; revised April 29, 2005. Posted online: 2005-12-12. Recommended by Associate Editor I. Kolmanovsky. This work was supported by the Swedish Research Council under Project 20005630 and by the Swedish Foundation for Strategic Research under Project CPDC.
Subject Keywords:Bode sensitivity integral, linear time-periodic systems, performance limitations
Issue or Number:12
Record Number:CaltechAUTHORS:SANieeetac05b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1287
Deposited By: Archive Administrator
Deposited On:08 Jan 2006
Last Modified:08 Nov 2021 19:09

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