### Abstract

Owing to its superior performance in high-speed signal processing/control, work on delta-operator based discrete time system implementations have attracted considerable attention. Stability and performance of such a system is closely related to the root distribution of its characteristic equation with respect to a certain `shifted' circle in the complex plane; the underlying sampling time determines its centre and radius. An algorithm that checks root distribution of a given polynomial with respect to this stability boundary is proposed. It is based on a scaled version of the well known Marden-Jury table that determines root distribution with respect to the unit circle in the complex plane; this is the stability boundary corresponding to discrete time systems that are implemented using the more conventional shift operator. The Marden-Jury table offers several additional advantages that are not all present in other available algorithms applicable to shift operator based polynomials. The proposed algorithm possesses all these properties, and the scaling scheme used ensures improved numerical accuracy and the existence of a limiting form.

Original language | English |
---|---|

Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | IEE Proceedings: Control Theory and Applications |

Volume | 147 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2000 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering
- Instrumentation

### Cite this

*IEE Proceedings: Control Theory and Applications*,

*147*(1), 1-12. https://doi.org/10.1049/ip-cta:20000144

**Root distribution of delta-operator formulated polynomials.** / Premaratne, Kamal; Touset, S.; Jury, E. I.

Research output: Contribution to journal › Article

*IEE Proceedings: Control Theory and Applications*, vol. 147, no. 1, pp. 1-12. https://doi.org/10.1049/ip-cta:20000144

}

TY - JOUR

T1 - Root distribution of delta-operator formulated polynomials

AU - Premaratne, Kamal

AU - Touset, S.

AU - Jury, E. I.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - Owing to its superior performance in high-speed signal processing/control, work on delta-operator based discrete time system implementations have attracted considerable attention. Stability and performance of such a system is closely related to the root distribution of its characteristic equation with respect to a certain `shifted' circle in the complex plane; the underlying sampling time determines its centre and radius. An algorithm that checks root distribution of a given polynomial with respect to this stability boundary is proposed. It is based on a scaled version of the well known Marden-Jury table that determines root distribution with respect to the unit circle in the complex plane; this is the stability boundary corresponding to discrete time systems that are implemented using the more conventional shift operator. The Marden-Jury table offers several additional advantages that are not all present in other available algorithms applicable to shift operator based polynomials. The proposed algorithm possesses all these properties, and the scaling scheme used ensures improved numerical accuracy and the existence of a limiting form.

AB - Owing to its superior performance in high-speed signal processing/control, work on delta-operator based discrete time system implementations have attracted considerable attention. Stability and performance of such a system is closely related to the root distribution of its characteristic equation with respect to a certain `shifted' circle in the complex plane; the underlying sampling time determines its centre and radius. An algorithm that checks root distribution of a given polynomial with respect to this stability boundary is proposed. It is based on a scaled version of the well known Marden-Jury table that determines root distribution with respect to the unit circle in the complex plane; this is the stability boundary corresponding to discrete time systems that are implemented using the more conventional shift operator. The Marden-Jury table offers several additional advantages that are not all present in other available algorithms applicable to shift operator based polynomials. The proposed algorithm possesses all these properties, and the scaling scheme used ensures improved numerical accuracy and the existence of a limiting form.

UR - http://www.scopus.com/inward/record.url?scp=0033873535&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033873535&partnerID=8YFLogxK

U2 - 10.1049/ip-cta:20000144

DO - 10.1049/ip-cta:20000144

M3 - Article

VL - 147

SP - 1

EP - 12

JO - IEE Proceedings: Control Theory and Applications

JF - IEE Proceedings: Control Theory and Applications

SN - 1350-2379

IS - 1

ER -