Responses of positive standard and fractional linear systems and electrical circuits with derivatives of their inputs

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.24425/124257

• Języki publikacji: EN

Abstrakty

EN

Responses of positive standard and fractional continuous-time and discrete-time linear systems with derivatives of their inputs are presented herein. It is shown that the formulae for state vectors and outputs are also valid for their derivatives if the inputs and outputs and their derivatives of suitable order are zero for t = 0. Similar results are also shown for positive standard and fractional discrete-time linear systems.

Słowa kluczowe

EN

positive fractional linear system; continuous-time; discrete-time; response formula

PL

dyskretny czas; układ ułamkowy; ciągłość czasowa

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2018
• Tom: Vol. 66, nr 4
• Strony: 419--425
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• [1] L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley, New York 2000.
• [2] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2001.
• [3] T. Kaczorek, “Descriptor positive discrete-time and continuous-time nonlinear systems”, Proc. of SPIE, vol. 9290, 2014, doi:10.1117/12.2074558.
• [4] T. Kaczorek, “Positivity and linearization of a class of nonlinear discrete-time systems by state feedbacks”, Logistyka 6, 5078–5083 (2014).
• [5] T. Kaczorek, “Positive descriptor discrete-time linear systems”, Problems of Nonlinear Analysis in Engineering Systems 1(7), 38–54 (1998).
• [6] T. Kaczorek, “Positive linear systems consisting of n subsystems with different fractional orders”, IEEE Trans. Circuits and Systems 58(6), 1203–1210 (2011).
• [7] T. Kaczorek, “Positivity and stability of discrete-time nonlinear systems”, 2015 IEEE 2nd International Conference on Cybernetics (CYBCONF), Gdynia, 2015, pp. 156–159.
• [8] T. Kaczorek, “Positive singular discrete time linear systems”, Bull. Pol. Ac.: Tech. 45(4), 619–631 (1997).
• [9] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin 2012.
• [10] T. Kaczorek, Linear Control Systems, Vol. 1, J. Wiley, New York 1999.
• [11] H. Zhang, D. Xie, H. Zhang, and G. Wang, “Stability analysis for discrete-time switched systems with unstable subsystems by a mode-dependent average dwell time approach”, ISA Transactions 53, 1081–1086 (2014).
• [12] J. Zhang, Z. Han, H. Wu, and J. Hung, “Robust stabilization of discrete-time positive switched systems with uncertainties and average dwell time switching”, Circuits Syst. Signal Process. 33, 71–95 (2014).
• [13] J. Losada and J. Nieto, “Properties of a new fractional derivative without singular kernel”, Progr. Fract. Differ. Appl. 1(2), 87–92 (2015).
• [14] P.J. Antsaklis and A.N. Michel, Linear Systems, Birkhauser, Boston 2006.
• [15] H. Rosenbrock, State-Space and Multivariable Theory, J. Wiley, New York 1970.

Uwagi

PL

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