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

International Journal of Applied Mathematics and Computer Science

Volumn 22, Issue 3, 2012, Pages 533-538

  Ostalczyk, Piotr ^a  

^a LODZ UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Fractional Calculus; Linear Discrete Time System; Stability Domain

Indexed keywords

DISCRETE SYSTEMS; FRACTIONAL CALCULUS; FRACTIONAL ORDER; FRACTIONAL-ORDER SYSTEMS; LINEAR DISCRETE-TIME SYSTEMS; STABILITY DOMAINS; STATE SPACE EQUATION; UNIT-STEP RESPONSE;

DIFFERENCE EQUATIONS;

LINEAR SYSTEMS;

EID: 84876695925     PISSN: None     EISSN: 1641876X     Source Type: Journal    
DOI: 10.2478/v10006-012-0040-7     Document Type: Article

References (15)

1. Dzielínski, 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. G?uvenç 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 L'od'z Press, L'od'z, (in Polish).
10. Oustaloup, A. (1991). La commande CRONE, ́editions Hermès, Paris.
11. Oustaloup, A. (1995). La derivation non entière: thèorie, syntheses et applications, ́ Editions Hermès, Paris.
12. Oustaloup, A. (1999). La commande crone: du scalaire au multivariable, ́ Editions 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. Vaĺerio, D. and Costa, S. (2006). Tuning of fractional PID controllers with Ziegler-Nichols-type rules, Signal Processing 86(10): 2771-2784.