# Improving the stability of discretization zeros with the Taylor method using a generalization of the fractional-order hold

Cheng Zeng; Shan Liang; Yuzhe Zhang; Jiaqi Zhong; Yingying Su

International Journal of Applied Mathematics and Computer Science (2014)

- Volume: 24, Issue: 4, page 745-757
- ISSN: 1641-876X

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topCheng Zeng, et al. "Improving the stability of discretization zeros with the Taylor method using a generalization of the fractional-order hold." International Journal of Applied Mathematics and Computer Science 24.4 (2014): 745-757. <http://eudml.org/doc/271883>.

@article{ChengZeng2014,

abstract = {Remarkable improvements in the stability properties of discrete system zeros may be achieved by using a new design of the fractional-order hold (FROH) circuit. This paper first analyzes asymptotic behaviors of the limiting zeros, as the sampling period T tends to zero, of the sampled-data models on the basis of the normal form representation for continuous-time systems with a new hold proposed. Further, we also give the approximate expression of limiting zeros of the resulting sampled-data system as power series with respect to a sampling period up to the third order term when the relative degree of the continuous-time system is equal to three, and the corresponding stability of the discretization zeros is discussed for fast sampling rates. Of particular interest are the stability conditions of sampling zeros in the case of a new FROH even though the relative degree of a continuous-time system is greater than two, whereas the conventional FROH fails to do so. An insightful interpretation of the obtained sampled-data model can be made in terms of minimal intersample ripple by design, where multirate sampled systems have a poor intersample behavior. Our results provide a more accurate approximation for asymptotic zeros, and certain known results on asymptotic behavior of limiting zeros are shown to be particular cases of the ideas presented here.},

author = {Cheng Zeng, Shan Liang, Yuzhe Zhang, Jiaqi Zhong, Yingying Su},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {stability; discretization zeros; Taylor method; signal reconstruction; sampled-data model},

language = {eng},

number = {4},

pages = {745-757},

title = {Improving the stability of discretization zeros with the Taylor method using a generalization of the fractional-order hold},

url = {http://eudml.org/doc/271883},

volume = {24},

year = {2014},

}

TY - JOUR

AU - Cheng Zeng

AU - Shan Liang

AU - Yuzhe Zhang

AU - Jiaqi Zhong

AU - Yingying Su

TI - Improving the stability of discretization zeros with the Taylor method using a generalization of the fractional-order hold

JO - International Journal of Applied Mathematics and Computer Science

PY - 2014

VL - 24

IS - 4

SP - 745

EP - 757

AB - Remarkable improvements in the stability properties of discrete system zeros may be achieved by using a new design of the fractional-order hold (FROH) circuit. This paper first analyzes asymptotic behaviors of the limiting zeros, as the sampling period T tends to zero, of the sampled-data models on the basis of the normal form representation for continuous-time systems with a new hold proposed. Further, we also give the approximate expression of limiting zeros of the resulting sampled-data system as power series with respect to a sampling period up to the third order term when the relative degree of the continuous-time system is equal to three, and the corresponding stability of the discretization zeros is discussed for fast sampling rates. Of particular interest are the stability conditions of sampling zeros in the case of a new FROH even though the relative degree of a continuous-time system is greater than two, whereas the conventional FROH fails to do so. An insightful interpretation of the obtained sampled-data model can be made in terms of minimal intersample ripple by design, where multirate sampled systems have a poor intersample behavior. Our results provide a more accurate approximation for asymptotic zeros, and certain known results on asymptotic behavior of limiting zeros are shown to be particular cases of the ideas presented here.

LA - eng

KW - stability; discretization zeros; Taylor method; signal reconstruction; sampled-data model

UR - http://eudml.org/doc/271883

ER -

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