## 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

Cheng Zeng, Shan Liang, and Yingying Su

#### 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

**Permanent link to this document**

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