<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

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

College of Science Guizhou Institute of Technology, No. 1 Caiguanlu, Yunyan, Guiyang Guizhou, 550003, China

College of Automation University of Chongqing, No. 174 Shazhengjie, Shapingba, Chongqing, 400044, China

Key Laboratory of Dependable Service Computing in Cyber Physical Society, Ministry of Education University of Chongqing, No. 174 Shazhengjie, Shapingba, Chongqing, 400044, China

College of Automation University of Chongqing, No. 174 Shazhengjie, Shapingba, Chongqing, 400044, Chin

Department of Electric and Electronic Information Engineering Chongqing University of Science and Technology, No. 20 Daxuecheng, Shapingba, Chongqing, 401331, China

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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....

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

Published Online: Dec 20, 2014

Page range: 745 - 757

Received: Aug 06, 2013

DOI: https://doi.org/10.2478/amcs-2014-0055

© by Cheng Zeng

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.