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Frequency-Domain Analysis of Linear Time-Periodic Systems

Sandberg, Henrik and Möllerstedt, Erik and Bernhardsson, Bo (2005) Frequency-Domain Analysis of Linear Time-Periodic Systems. IEEE Transactions on Automatic Control, 50 (12). pp. 1971-1983. ISSN 0018-9286. doi:10.1109/TAC.2005.860294.

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In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature.

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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 10, 2004; revised June 2, 2005. Posted online: 2005-12-12. Recommended by Associate Editor U. Jonsson. This work was supported by the Swedish Research Council under Project 20005630, and by the Swedish Foundation for Strategic Research under Project CPDC. The authors would like to thank J. Malinen, A. Rantzer, and K.J. Åström for fruitful discussions and suggestions. The first author spent the spring of 2003 at the Mittag–Leffler Institute, Stockholm, Sweden, and he is thankful to the institute and its staff.
Subject Keywords:Convergence analysis, frequency-response operators, linear time-periodic systems, series expansions
Issue or Number:12
Record Number:CaltechAUTHORS:SANieeetac05a
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1286
Deposited By: Archive Administrator
Deposited On:08 Jan 2006
Last Modified:08 Nov 2021 19:09

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