Analysis of positive and stable fractional continuous-time linear systems by the use of Caputo Fabrizio derivative

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

Using the Caputo-Fabrizio definition of fractional order derivative, the positivity and asymptotic stability of the fractional continuous-time linear systems are investigated. The solution to the matrix fractional differential state equations is derived. Necessary and sufficient conditions for the positivity and asymptotic stability of the fractional linear systems are established. Tests for checking of the asymptotic stability of the systems are provided.

Słowa kluczowe

EN

analysis; Caputo-Fabrizio definition; fractional; linear; positivity; stability; system

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2016
• Tom: Vol. 45, no. 3
• Strony: 289--299
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Bialystok University of Technology, Bialystok, Poland

Bibliografia

• [1] Farina, L. and Rinaldi, S. (2000) Positive Linear Systems; Theory and Applications. Wiley, New York. Gantmacher, F. R. (1959) The Theory of Matrices. Chelsea Publishing Company, New York.
• [2] Kaczorek, T. (2015) Positivity and stability of discrete-time nonlinear systems. In: Proceedings of the 2nd International Conference on Cybernetics, CYBCONF, June 24-26, Gdynia, Poland.
• [3] Kaczorek, T. (2014a) Descriptor positive discrete-time and continuous-time nonlinear systems. Proceedings of SPIE, 9290 DOI:10.1117/12.2074558.
• [4] Kaczorek, T. (2014b) Positivity and linearization of a class of nonlinear discrete-time systems by state feedbacks. Logistyka 6, 5078-5083.
• [5] Kaczorek, T. (2012) Selected Problems of Fractional Systems Theory. LNCIS 411, Springer-Verlag. Kaczorek, T. (2011a) New stability tests of positive standard and fractional linear systems. Circuits and Systems 2(6), 261-268.
• [6] Kaczorek, T. (2011b) Positive linear systems consisting of n subsystems with different fractional orders. IEEE Transactions on Circuits and Systems 58(8), 1203-1210.
• [7] Kaczorek, T. (2002) Positive 1D and 2D Systems. Springer-Verlag, London. Kaczorek, T. (1998) Positive descriptor discrete-time linear systems. Problems of Nonlinear Analysis in Engineering Systems 1(9), 38-54.
• [8] Kaczorek, T. (1997) Positive singular discrete time linear systems. Bulletin of the Polish Academy of Sciences; Technical Sciences 45(6), 619-631.
• [9] Losada, J. and Nieto, J. (2015) Properties of a new fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications 1(2), 87-92.
• [10] Zhang, H., Xie, D., Zhang, H. and Wang, G. (2014a) Stability analysis for discrete-time switched systems with unstable subsystems by a modedependent average dwell time approach. ISA Transactions 53, 1081-1086.
• [11] Zhang, J., Han, Z., Wu, H. and Hung, J. (2014b) Robust stabilization of discrete-time positive switched systems with uncertainties and average dwell time switching. Circuits, Systems and Signal Processing 33, 71-95.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).