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

International Journal of Applied Mathematics and Computer Science (2012)

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

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topPiotr 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

top- 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
- 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
- Kaczorek, T. (2011). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin. Zbl1221.93002
- Kailath, S. (1980). Linear Systems, Prentice-Hall, Englewood Cliffs, NJ. Zbl0454.93001
- Matignon, D. (1996). Stability results for fractional differential eqations with applications to control processing, Computational Engineering in Systems and Application Multiconference, Lille, France, pp. 963-968.
- Miller, K. and Ross, B. (1993). An Introduction to Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY. Zbl0789.26002
- Ogata, K. (1987). Discrete Control Systems, Prentice-Hall, Englewood Cliffs, NJ.
- Oldham, K. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY. Zbl0292.26011
- Ostalczyk, P. (2008). Epitome of Fractional Calculus: Theory and Its Applications in Automatics, Technical University of Łódź Press, Łódź, (in Polish).
- Oustaloup, A. (1991). La commande CRONE, Éditions Hermès, Paris.
- Oustaloup, A. (1995). La derivation non entière: thèorie, syntheses et applications, Éditions Hermès, Paris.
- Oustaloup, A. (1999). La commande crone: du scalaire au multivariable, Éditions Hermès, Paris.
- Podlubny, I. (1999). Fractional Differential Equations, Academic Press, New York, NY. Zbl0924.34008
- Samko, A. Kilbas, A. and Marichev, O. (1993). Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, London. Zbl0818.26003
- Valério, D. and Costa, S. (2006). Tuning of fractional PID controllers with Ziegler-Nichols-type rules, Signal Processing 86(10): 2771-2784. Zbl1172.94496

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