Sampling zeros and the Euler-Frobenius polynomials

Author

Weller, Steven R. ; Moran, W. ; Ninness, Brett ; Pollington, A.D.

Author_Institution

Dept. of Electr. & Comput. Eng., Newcastle Univ., NSW, Australia

Volume

46

Issue

2

fYear

2001

fDate

2/1/2001 12:00:00 AM

Firstpage

340

Lastpage

343

Abstract

We show that the zeros of sampled-data systems resulting from rapid sampling of continuous-time systems preceded by a zero-order hold (ZOH) are the roots of the Euler-Frobenius polynomials. Using known properties of these polynomials, we prove two conjectures of Hagiwara et al. (1993), the first of which concerns the simplicity, negative realness, and interlacing properties of the sampling zeros of ZOH- and first-order hold (FOH-) sampled systems. To prove the second conjecture, we show that in the fast sampling limit, and as the continuous-time relative degree increases, the largest sampling zero for FOH-sampled systems approaches 1/e, where e is the base of the natural logarithm

Keywords

continuous time systems; poles and zeros; polynomials; sampled data systems; Euler-Frobenius polynomials; continuous-time systems; fast sampling limit; first-order hold systems; interlacing properties; negative realness; rapid sampling; sampling zeros; simplicity; zero-order hold; Australia Council; Extrapolation; Mathematics; Poles and zeros; Polynomials; Sampling methods; Statistics; Transfer functions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.905706

Filename

905706