Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.

Słowa kluczowe

EN

Pade approximation; fractional system; linear positive system

PL

aproksymacja Padégo; układ ułamkowy; układ liniowy dodatni

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2013
• Tom: Vol. 23, no. 3
• Strony: 501--506
• Opis fizyczny: Bibliogr. 12 poz., wykr.

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Białystok Technical University, ul. Wiejska 45D, 15-351 Białystok, Poland

Bibliografia

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• [3] Busłowicz, M. (2012). Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(2): 279–284.
• [4] Busłowicz, M. and Kaczorek, T. (2009). Simple conditions for practical stability of positive fractional discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 19(2): 263–269, DOI: 10.2478/v10006-009-0022-6.
• [5] Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY.
• [6] Gantmakher, F.R. (1959). Theory of Matrices, Chelsea Pub. Co., New York, NY.
• [7] Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.
• [8] Kaczorek, T. (1999). Relationship between the value of discretisation step and positivity and stabilization of linear dynamic systems, Proceedings of the Conference on Simulation, Designing and Control of Foundry Processes, Kraków, Poland, pp. 33–39.
• [9] Kaczorek, T. (1998). Vectors and Matrices in Automation and Electrotechnics, WNT, Warsaw, (in Polish).
• [10] Kaczorek, T. (2011). Selected Problems of Fractional System Theory, Springer-Verlag, Berlin.
• [11] Kaczorek, T. (2013). Approximation of positive stable continuous-time linear systems by positive stable discrete-time systems, Pomiary Automatyka Robotyka 59 (2): 359–364.
• [12] Kaczorek, T. (2011). Necessary and sufficient conditions of stability of fractional positive continuous-time linear systems, Acta Mechanica et Automatica 5(2): 52–54.