Design of unknown input fractional-order observers for fractional-order systems

Ibrahima N'Doye; Mohamed Darouach; Holger Voos; Michel Zasadzinski

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 3, page 491-500
  • ISSN: 1641-876X

Abstract

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This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1 ≤ α < 2 and 0 < α ≤ 1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.

How to cite

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Ibrahima N'Doye, et al. "Design of unknown input fractional-order observers for fractional-order systems." International Journal of Applied Mathematics and Computer Science 23.3 (2013): 491-500. <http://eudml.org/doc/262395>.

@article{IbrahimaNDoye2013,
abstract = {This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1 ≤ α < 2 and 0 < α ≤ 1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.},
author = {Ibrahima N'Doye, Mohamed Darouach, Holger Voos, Michel Zasadzinski},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {fractional calculus; fractional-order systems; fractional-order observers; existence condition; linear matrix inequality; unknown input; stability},
language = {eng},
number = {3},
pages = {491-500},
title = {Design of unknown input fractional-order observers for fractional-order systems},
url = {http://eudml.org/doc/262395},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Ibrahima N'Doye
AU - Mohamed Darouach
AU - Holger Voos
AU - Michel Zasadzinski
TI - Design of unknown input fractional-order observers for fractional-order systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 3
SP - 491
EP - 500
AB - This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1 ≤ α < 2 and 0 < α ≤ 1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.
LA - eng
KW - fractional calculus; fractional-order systems; fractional-order observers; existence condition; linear matrix inequality; unknown input; stability
UR - http://eudml.org/doc/262395
ER -

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