Statistical Analysis and H 2 - Norm of Finite Dimensional Linear Time-Periodic Systems

Lampe, Bernhard P.; Rosenwasser, Efim N.

doi:10.1016/s1474-6670(17)34053-3

Cited by 10 publications

(9 citation statements)

References 7 publications

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“…To see that is the maximum input roll-off, assume has a larger roll-off . Then, we obtain a contradiction for sufficiently large in (13) due to the lower bound.…”

Section: I)mentioning

confidence: 88%

“…The infinite dimensionality can be seen as the price that is paid for the removal of the time dependence in the transfer function. For example, it was shown in [13] that a Fourier expansion of the PTF in the time direction yields the elements of the HTF.…”

Section: A Previous Workmentioning

confidence: 99%

“…If this time dependence is expressed in an harmonic basis of the type , we essentially obtain the HTF. Relations of this sort are treated in [13]- [15]. In this paper, we investigate what happens when higher harmonics in this basis are truncated.…”

Section: A Previous Workmentioning

confidence: 99%

“…We use them in the following theorem to show that the Markov parameters in Definition 2 determine the roll-off. (13) and the system has input roll-off . To see that is the maximum input roll-off, assume has a larger roll-off .…”

Section: I)mentioning

confidence: 99%

“…The price is that the HTF becomes infinite dimensional. The relation between the PTF and the HTF has also been discussed in [13].…”

Section: Example 3 (Harmonic Response and The Ptf)mentioning

confidence: 99%

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Frequency-domain analysis of linear time-periodic systems

Sandberg

Möllerstedt²,

Bernhardsson

2005

IEEE Trans. Automat. Contr.

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Abstract-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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“…To see that is the maximum input roll-off, assume has a larger roll-off . Then, we obtain a contradiction for sufficiently large in (13) due to the lower bound.…”

Section: I)mentioning

confidence: 88%

Section: A Previous Workmentioning

confidence: 99%