Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains

Piotr Ostalczyk

International Journal of Applied Mathematics and Computer Science (2012)

  • Volume: 22, Issue: 3, page 533-538
  • ISSN: 1641-876X

Abstract

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Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented.

How to cite

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Piotr Ostalczyk. "Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains." International Journal of Applied Mathematics and Computer Science 22.3 (2012): 533-538. <http://eudml.org/doc/244067>.

@article{PiotrOstalczyk2012,
abstract = {Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented.},
author = {Piotr Ostalczyk},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {fractional calculus; linear discrete-time system; stability domain},
language = {eng},
number = {3},
pages = {533-538},
title = {Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains},
url = {http://eudml.org/doc/244067},
volume = {22},
year = {2012},
}

TY - JOUR
AU - Piotr Ostalczyk
TI - Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains
JO - International Journal of Applied Mathematics and Computer Science
PY - 2012
VL - 22
IS - 3
SP - 533
EP - 538
AB - Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented.
LA - eng
KW - fractional calculus; linear discrete-time system; stability domain
UR - http://eudml.org/doc/244067
ER -

References

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  1. Dzieliński, A. and Sierociuk, D. (2008). Stability of discrete fractional order state-space systems, Journal of Vibration and Control 14(9/10): 1543-1556. Zbl1229.93143
  2. Guermah, S., Djennoune, S. and Bettayeb, M. (2010). A new approach for stability analysis of linear discrete-time fractional-order systems, in D. Baleanu, Z. Güvenç and J.T. Machado (Eds.), New Trends in Nanotechnology and Fractional Calculus Applications, Springer, Dodrecht, pp. 151-162. Zbl1206.93095
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  9. Ostalczyk, P. (2008). Epitome of Fractional Calculus: Theory and Its Applications in Automatics, Technical University of Łódź Press, Łódź, (in Polish). 
  10. Oustaloup, A. (1991). La commande CRONE, Éditions Hermès, Paris. 
  11. Oustaloup, A. (1995). La derivation non entière: thèorie, syntheses et applications, Éditions Hermès, Paris. 
  12. Oustaloup, A. (1999). La commande crone: du scalaire au multivariable, Éditions Hermès, Paris. 
  13. Podlubny, I. (1999). Fractional Differential Equations, Academic Press, New York, NY. Zbl0924.34008
  14. Samko, A. Kilbas, A. and Marichev, O. (1993). Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, London. Zbl0818.26003
  15. Valério, D. and Costa, S. (2006). Tuning of fractional PID controllers with Ziegler-Nichols-type rules, Signal Processing 86(10): 2771-2784. Zbl1172.94496

Citations in EuDML Documents

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  1. Messaoud Amairi, Recursive set membership estimation for output-error fractional models with unknown-but-bounded errors
  2. Cheng Zeng, Shan Liang, Yuzhe Zhang, Jiaqi Zhong, Yingying Su, Improving the stability of discretization zeros with the Taylor method using a generalization of the fractional-order hold
  3. Małgorzata Wyrwas, Ewa Pawluszewicz, Ewa Girejko, Stability of nonlinear h -difference systems with n fractional orders
  4. Grigory M. Sklyar, Grzegorz Szkibiel, Controlling a non-homogeneous Timoshenko beam with the aid of the torque

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