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Journal of Applied Mathematics
Volume 2013, Article ID 268684, 16 pages
Research Article

Improving the Asymptotic Properties of Discrete System Zeros in Fractional-Order Hold Case

1College of Automation, Chongqing University, Chongqing 400044, China
2Department of Mathematics, Guiyang University, Guiyang 550005, China
3Key Laboratory of Dependable Service Computing in Cyber Physical Society Ministry of Education, Chongqing University, Chongqing 400044, China
4Department of Electric and Electronic Information Engineering, Chongqing University of Science and Technology, Chongqing 401331, China

Received 17 July 2013; Revised 11 October 2013; Accepted 21 October 2013

Academic Editor: Baocang Ding

Copyright © 2013 Cheng Zeng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Remarkable improvements in the asymptotic properties of discrete system zeros may be achieved by properly adjusted fractional-order hold (FROH) circuit. This paper analyzes asymptotic properties of the limiting zeros, as the sampling period tends to zero, of the sampled-data models on the basis of the normal form representation of the continuous-time systems with FROH. Moreover, when the relative degree of the continuous-time system is equal to one or two, an approximate expression of the limiting zeros for the sampled-data system with FROH is also given as power series with respect to a sampling period up to the third-order term. And, further, the corresponding stability conditions of the sampling zeros are discussed for fast sampling rates. The ideas of the paper here provide a more accurate approximation for asymptotic zeros, and certain known achievements on asymptotic behavior of limiting zeros are shown to be particular cases of the results presented.