Geodesic
Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains
International Journal of Applied Mathematics and Computer Science, Tome 22 (2012) no. 3, pp. 533-538.

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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.
Keywords: fractional calculus, linear-discrete time system, stability domain
Mots-clés : rachunek ułamkowy, system dyskretno-czasowy, system liniowy 
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Ostalczyk, P. Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains. International Journal of Applied Mathematics and Computer Science, Tome 22 (2012) no. 3, pp. 533-538. http://geodesic.mathdoc.fr/item/IJAMCS_2012_22_3_a2/

[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.

[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.

[3] Kaczorek, T. (2011). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.

[4] Kailath, S. (1980). Linear Systems, Prentice-Hall, Englewood Cliffs, NJ.

[5] 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.

[6] Miller, K. and Ross, B. (1993). An Introduction to Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY.

[7] Ogata, K. (1987). Discrete Control Systems, Prentice-Hall, Englewood Cliffs, NJ.

[8] Oldham, K. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY.

[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.

[14] Samko, A. Kilbas, A. and Marichev, O. (1993). Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, London.

[15] Valério, D. and Costa, S. (2006). Tuning of fractional PID controllers with Ziegler-Nichols-type rules, Signal Processing 86(10): 2771-2784.