An iterative identification of pole-stucture in dynamic systems based on hyperbolic metrics and Malmquist-Takenaka representation

Alexandros Soumelidis, J. Bokor, Ferenc Schipp

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

In a series of paper the authors proposed a new frequency-domain approach to identify poles in discrete- Time linear systems. The discrete rational transfer function is represented in a rational Laguerre-basis, where the basis elements are expressed by powers of the Blaschke-function. This function can be interpreted as a congruence transform on the Poincaŕe unit disc model of the hyperbolic geometry. The identification of a pole is given as a hyperbolic transform of the limit of a quotient-sequence formed from the Laguerre-Fourier coefficients. This paper extends this approach by defining an iterative procedure to explore the pole structure. This is based on the successive elimination of the already identified poles by using the Malmquist-Takenaka representation of the discrete transfer function. The proposed procedure is suitable not only for structure estimation with no need of a priori assumption on the pole locations but knowing the poles it serves also as a basis for linear estimation of the residues or numerator coefficients in a rational orthogonal basis.

Original languageEnglish
Title of host publicationProceedings of the IEEE Conference on Decision and Control
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5180-5185
Number of pages6
ISBN (Print)9781467357173
DOIs
Publication statusPublished - 2013
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: Dec 10 2013Dec 13 2013

Other

Other52nd IEEE Conference on Decision and Control, CDC 2013
CountryItaly
CityFlorence
Period12/10/1312/13/13

Fingerprint

Hyperbolic Metric
Dynamic Systems
Pole
Poles
Dynamical systems
Transfer Function
Transfer functions
Transform
Lobachevskian geometry
Linear Estimation
Discrete-time Linear Systems
Orthogonal Basis
Rational functions
Numerator
Fourier coefficients
Iterative Procedure
Rational function
Unit Disk
Congruence
Frequency Domain

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

Soumelidis, A., Bokor, J., & Schipp, F. (2013). An iterative identification of pole-stucture in dynamic systems based on hyperbolic metrics and Malmquist-Takenaka representation. In Proceedings of the IEEE Conference on Decision and Control (pp. 5180-5185). [6760703] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760703

An iterative identification of pole-stucture in dynamic systems based on hyperbolic metrics and Malmquist-Takenaka representation. / Soumelidis, Alexandros; Bokor, J.; Schipp, Ferenc.

Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc., 2013. p. 5180-5185 6760703.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Soumelidis, A, Bokor, J & Schipp, F 2013, An iterative identification of pole-stucture in dynamic systems based on hyperbolic metrics and Malmquist-Takenaka representation. in Proceedings of the IEEE Conference on Decision and Control., 6760703, Institute of Electrical and Electronics Engineers Inc., pp. 5180-5185, 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, 12/10/13. https://doi.org/10.1109/CDC.2013.6760703
Soumelidis A, Bokor J, Schipp F. An iterative identification of pole-stucture in dynamic systems based on hyperbolic metrics and Malmquist-Takenaka representation. In Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc. 2013. p. 5180-5185. 6760703 https://doi.org/10.1109/CDC.2013.6760703
Soumelidis, Alexandros ; Bokor, J. ; Schipp, Ferenc. / An iterative identification of pole-stucture in dynamic systems based on hyperbolic metrics and Malmquist-Takenaka representation. Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc., 2013. pp. 5180-5185
@inproceedings{8ff7fc09b875416c88a0dfcf2ac49e4b,
title = "An iterative identification of pole-stucture in dynamic systems based on hyperbolic metrics and Malmquist-Takenaka representation",
abstract = "In a series of paper the authors proposed a new frequency-domain approach to identify poles in discrete- Time linear systems. The discrete rational transfer function is represented in a rational Laguerre-basis, where the basis elements are expressed by powers of the Blaschke-function. This function can be interpreted as a congruence transform on the Poincaŕe unit disc model of the hyperbolic geometry. The identification of a pole is given as a hyperbolic transform of the limit of a quotient-sequence formed from the Laguerre-Fourier coefficients. This paper extends this approach by defining an iterative procedure to explore the pole structure. This is based on the successive elimination of the already identified poles by using the Malmquist-Takenaka representation of the discrete transfer function. The proposed procedure is suitable not only for structure estimation with no need of a priori assumption on the pole locations but knowing the poles it serves also as a basis for linear estimation of the residues or numerator coefficients in a rational orthogonal basis.",
author = "Alexandros Soumelidis and J. Bokor and Ferenc Schipp",
year = "2013",
doi = "10.1109/CDC.2013.6760703",
language = "English",
isbn = "9781467357173",
pages = "5180--5185",
booktitle = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",

}

TY - GEN

T1 - An iterative identification of pole-stucture in dynamic systems based on hyperbolic metrics and Malmquist-Takenaka representation

AU - Soumelidis, Alexandros

AU - Bokor, J.

AU - Schipp, Ferenc

PY - 2013

Y1 - 2013

N2 - In a series of paper the authors proposed a new frequency-domain approach to identify poles in discrete- Time linear systems. The discrete rational transfer function is represented in a rational Laguerre-basis, where the basis elements are expressed by powers of the Blaschke-function. This function can be interpreted as a congruence transform on the Poincaŕe unit disc model of the hyperbolic geometry. The identification of a pole is given as a hyperbolic transform of the limit of a quotient-sequence formed from the Laguerre-Fourier coefficients. This paper extends this approach by defining an iterative procedure to explore the pole structure. This is based on the successive elimination of the already identified poles by using the Malmquist-Takenaka representation of the discrete transfer function. The proposed procedure is suitable not only for structure estimation with no need of a priori assumption on the pole locations but knowing the poles it serves also as a basis for linear estimation of the residues or numerator coefficients in a rational orthogonal basis.

AB - In a series of paper the authors proposed a new frequency-domain approach to identify poles in discrete- Time linear systems. The discrete rational transfer function is represented in a rational Laguerre-basis, where the basis elements are expressed by powers of the Blaschke-function. This function can be interpreted as a congruence transform on the Poincaŕe unit disc model of the hyperbolic geometry. The identification of a pole is given as a hyperbolic transform of the limit of a quotient-sequence formed from the Laguerre-Fourier coefficients. This paper extends this approach by defining an iterative procedure to explore the pole structure. This is based on the successive elimination of the already identified poles by using the Malmquist-Takenaka representation of the discrete transfer function. The proposed procedure is suitable not only for structure estimation with no need of a priori assumption on the pole locations but knowing the poles it serves also as a basis for linear estimation of the residues or numerator coefficients in a rational orthogonal basis.

UR - http://www.scopus.com/inward/record.url?scp=84902335897&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902335897&partnerID=8YFLogxK

U2 - 10.1109/CDC.2013.6760703

DO - 10.1109/CDC.2013.6760703

M3 - Conference contribution

AN - SCOPUS:84902335897

SN - 9781467357173

SP - 5180

EP - 5185

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Institute of Electrical and Electronics Engineers Inc.

ER -