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Frequency-Domain Analysis of Linear Time-Periodic Systems

Publiceringsår: 2005
Språk: Engelska
Sidor: 1971-1983
Publikation/Tidskrift/Serie: IEEE Transactions on Automatic Control
Volym: 50
Nummer: 12
Dokumenttyp: Artikel i tidskrift
Förlag: IEEE--Institute of Electrical and Electronics Engineers Inc.


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.


  • Control Engineering
  • series expansions
  • frequency-response operators
  • Convergence analysis
  • linear time-periodic systems


  • ISSN: 0018-9286

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