- Title
- Sampling zeros and the Euler-Frobenius polynomials
- Creator
- Weller, Steven R.; Moran, W.; Ninness, Brett; Pollington, A. D.
- Relation
- IEEE Transactions on Automatic Control Vol. 46 , Issue 2, p. 340-343
- Publisher Link
- http://dx.doi.org/10.1109/9.905706
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Resource Type
- journal article
- Date
- 2001
- Description
- 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.
- Subject
- continuous time systems; poles and zeros; polynomials; sampled data systems
- Identifier
- uon:857
- Identifier
- http://hdl.handle.net/1959.13/26395
- Identifier
- ISSN:0018-9286
- Rights
- Copyright © 2001 IEEE. Reprinted from IEEE Transactions on Automatic Control, Vol. 46, Issue 2, p. 340-343. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Newcastle's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
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