Positive electrical circuits with zero transfer matrices and their discretization

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.21008/j.1508-4248.2016.0001

• Języki publikacji: EN

Abstrakty

EN

Positive continuous–time and discrete–time linear electrical circuits with zero transfer matrices are addressed. It is shown that there exists a large class of positive electrical circuits with zero transfer matrices. The electrical circuits are unreachable, unobservable and unstable for all values of the resistances, inductances and capacitances. The discrete–time linear positive electrical circuits are introduced. It is shown that: 1) the discrete–time electrical circuit is asymptotically stable for all values of the discretization step if and only if the corresponding continuous–time electrical circuit is asymptotically stable; 2) the discretization of the continuous–time electrical circuit does not change their reachability, observability and transfer matrices.

Słowa kluczowe

EN

positive electrical circuit; reachability; observability; stability; discretization; transfer matrix

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Computer Applications in Electrical Engineering
• Rocznik: 2016
• Tom: Vol. 14
• Strony: 1--13
• Opis fizyczny: Bibliogr. 27 poz., rys.

Twórcy

autor

Kaczorek T.

• Bialystok University of Technology

Bibliografia

• [1] Antsaklis E., Michel A., Linear Systems, Birkhauser, Boston, 2006.
• [2] Busłowicz M., Stability of linear continuous–time fractional order systems with delays of the retarded type, Bull. Pol. Acad. Sci. Tech., vol. 56, no. 4, pp. 319–324, 2008.
• [3] Dzieliński A., Sierociuk D., Stability of discrete fractional order state–space systems, Journal of Vibrations and Control, vol. 14, no. 9–10, pp. 1543–1556, 2008.
• [4] Dzieliński A., Sierociuk D., Sarwas G., Ultracapacitor parameters identification based on fractional order model, Proc. European Control Conference, Budapest, Hungary, 2009.
• [5] Farina L., Rinaldi S., Positive Linear Systems: Theory and Applications, J. Wiley & Sons, New York, 2000.
• [6] Kaczorek T., Asymptotic stability of positive fractional 2D linear systems, Bull. Pol. Acad. Sci. Tech., vol. 57, no. 3, pp. 289–292, 2009.
• [7] Kaczorek T., Constructability and observability of standard and positive electrical circuits, Electrical Review, vol. 89, no. 7, pp. 132–136, 2013.
• [8] Kaczorek T., Controllability and observability of linear electrical circuits, Electrical Review, vol. 87, no. 9a, pp. 248–254, 2011.
• [9] Kaczorek T., Decomposition of the pairs (A,B) and (A,C) of the positive discrete–time linear systems, Archives of Control Sciences, vol. 20, no. 3, pp. 341–361, 2010.
• [10] Kaczorek T., Decoupling zeros of positive discrete–time linear systems, Circuits and Systems, vol. 1, pp. 41–48, 2010.
• [11] Kaczorek T., Fractional positive continuous–time linear systems and their reachability, Int. J. Appl. Math. Comput. Sci., vol. 18, no. 2, pp. 223–228, 2008.
• [12] Kaczorek T., Positive 1D and 2D Systems, London, UK: Springer–Verlag, 2002.
• [13] Kaczorek T., Positive electrical circuits and their reachability, Archives of Electrical Engineering, vol. 60, no. 3, pp. 283–301, 2011.
• [14] Kaczorek T., Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. Circuits and Systems, vol. 58, no. 6, pp. 1203–1210, 2011.
• [15] Kaczorek T., Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica, vol. 5, no. 2, pp. 42–51, 2011.
• [16] Kaczorek T., Practical stability of positive fractional discrete–time linear systems, Bull. Pol. Acad. Sci. Tech., vol. 56, no. 4, pp. 313–317, 2008.
• [17] Kaczorek T., Reachability and controllability to zero tests for standard and positive fractional discrete–time systems, Journal Européen des Systemes Automatisés, JESA, vol. 42, no. 6–8, pp. 769–787, 2008.
• [18] Kaczorek T., Reachability and observablity of fractional positive continuous–time linear systems, Proc. XV Conf. System Modelling and Control, Sept. 23–24, Lodz, Poland, 2013.
• [19] Kaczorek T., Reachability and observability of fractional positive electrical circuits, Computational Problems of Electrical Engineering, vol. 3, no. 2, pp. 28–36, 2013.
• [20] Kaczorek T., Selected Problems of Fractional Systems Theory, Berlin, Germany: Springer–Verlag, 2011.
• [21] Kaczorek T., Stability of positive continuous–time systems with delays, Bull. Pol. Acad. Sci. Tech., vol. 57, no. 4, pp. 395–398, 2009.
• [22] Kaczorek T., Standard and positive electrical circuits with zero transfer matrices, Poznan University of Technology Academic Journals: Electrical Engineering, no. 85, pp. 11–28, 2016.
• [23] Kaczorek T., Rogowski K., Fractional Linear Systems and Electrical Circuits, Studies in Systems, Decision and Control, vol. 13, Springer, 2015.
• [24] Kailath T., Linear systems, Prentice Hall, Englewood Cliffs, New York, 1980.
• [25] Kalman R., Mathematical description of linear systems, SIAM J. Control, vol. 1, no. 2, pp. 152–192, 1963.
• [26] Kalman R., On the general theory of control systems, Proc. First Intern. Congress on Automatic Control, London, UK: Butterworth, pp. 481–493, 1960.
• [27] Rosenbrock H., State–space and multivariable theory, New York, USA: J. Wiley, 1970.

Uwagi

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