Analysis of positive linear continuous-time systems using the conformable derivative

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.2478/amcs-2018-0024

• Języki publikacji: EN

Abstrakty

EN

Positive linear continuous-time systems are analyzed via conformable fractional calculus. A solution to a fractional linear system is derived. Necessary and sufficient conditions for the positivity of linear systems are established. Necessary and sufficient conditions for the asymptotic stability of positive linear systems are also given. The solutions of positive fractional linear systems based on the Caputo and conformable definitions are compared.

Słowa kluczowe

EN

conformable fractional derivative; positive linear system; system stability

PL

pochodna ułamkowa; układ liniowy dodatni; stabilność systemu

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2018
• Tom: Vol. 28, no. 2
• Strony: 335--340
• Opis fizyczny: Bibliogr. 19 poz., rys., wykr.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• [1] Abdeljawad, T. (2015). On conformable fractional calculus, Journal of Computational and Applied Mathematics 279: 57–66.
• [2] Benvenuti, L. and Farina, L. (2004). A tutorial on the positive realization problem, IEEE Transactions on Automatic Control 49(5): 651–664.
• [3] Farina, L. and Rinaldi, S. (2000). Positive Linear Systems, Theory and Applications, Wiley, New York, NY.
• [4] Kaczorek, T. (2016a). Minimal-phase positive electrical circuits, Electrical Review 92(3): 182–189.
• [5] Kaczorek, T. (2016b). Positive electrical circuits with zero transfer matrices and their discretization, Computer Applications in Electrical Engineering 14: 1–13.
• [6] Kaczorek, T. (2015a). A class of positive and stable time-varying electrical circuits, Electrical Review 91(5): 121–124.
• [7] Kaczorek, T. (2015b). Normal positive electrical circuits, IET Circuits Theory and Applications 9(5): 691–699.
• [8] Kaczorek, T. (2014). Decoupling zeros of positive continuous-time linear systems and electrical circuits, in J. Świątek et al. (Eds.), Advances in Systems Science, Springer, Cham, pp. 1–15.
• [9] Kaczorek, T. (2013a). Constructability and observability of standard and positive electrical circuits, Electrical Review 89(7): 132–136.
• [10] Kaczorek, T. (2013b). Positive fractional linear electrical circuits, Proceedings of SPIE 8903, Art. No. 3903-35.
• [11] Kaczorek, T. (2013c). Zeroing of state variables in descriptor electrical circuits by state-feedbacks, Electrical Review 89(10): 200–203.
• [12] Kaczorek, T. (2012). Positive unstable electrical circuits, Electrical Review 88(5a): 187–192.
• [13] Kaczorek, T. (2011a). Positive electrical circuits and their reachability, Archives of Electrical Engineering 60(3): 283–301.
• [14] Kaczorek, T. (2011b). Positive systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuits and Systems 58(6): 1203–1210.
• [15] Kaczorek, T. (2011c). Selected Problems of Fractional Systems Theory, Springer, Berlin.
• [16] Kaczorek, T. (2010). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(3): 453–458.
• [17] Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer, London.
• [18] Kaczorek, T. and Rogowski, K. (2015). Fractional Linear Systems and Electrical Circuits, Studies in Systems, Decision and Control, Vol. 13, Springer, Berlin.
• [19] Khalil R., Al Horani M., Yousef A., Sababheh M. (2014). A new definition of fractional derivative, Journal of Computational and Applied Mathematics 264: 65–70.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).