## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2013, Special Issue (2013), Article ID 268684, 16 pages.

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

#### Abstract

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 $T$ 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.

#### Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 268684, 16 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394806098

Digital Object Identifier
doi:10.1155/2013/268684

Zentralblatt MATH identifier
06950591

#### Citation

Zeng, Cheng; Liang, Shan; Su, Yingying. Improving the Asymptotic Properties of Discrete System Zeros in Fractional-Order Hold Case. J. Appl. Math. 2013, Special Issue (2013), Article ID 268684, 16 pages. doi:10.1155/2013/268684. https://projecteuclid.org/euclid.jam/1394806098

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