Singular fractional linear systems and electrical circuits

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches only with an ideal supercapacitor and voltage sources or at least one node with branches with supercoils.

Słowa kluczowe

EN

singular; fractional system; linear circuit; regular pencil; supercapacitor; supercoil

PL

system ułamkowy; układ liniowy; superkondensator

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2011
• Tom: Vol. 21, no 2
• Strony: 379--384
• Opis fizyczny: Bibliogr. 15 poz., rys.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• [1] Dodig, M. and Stosic, M. (2009). Singular systems state feedbacks problems, Linear Algebra and Its Applications 431(8): 1267-1292.
• [2] Dai, L. (1989). Singular Control Systems, Springer-Verlag, Berlin.
• [3] Fahmy, M. H and O'Reill J. (1989). Matrix pencil of closed-loop descriptor systems: Infinite-eigenvalues assignment, International Journal of Control 49(4): 1421-1431.
• [4] Gantmacher, F. R. (1960). The Theory of Matrices, Chelsea Publishing Co., New York, NY.
• [5] Kaczorek, T. (1992). Linear Control Systems, Vol. 1, Research Studies Press, John Wiley, New York, NY.
• [6] Kaczorek, T. (2004). Infinite eigenvalue assignment by output-feedbacks for singular systems, International Journal of Applied Mathematics and Computer Science 14(1): 19-23.
• [7] Kaczorek, T. (2007a). Polynomial and Rational Matrices. Applications in Dynamical Systems Theory, Springer-Verlag, London.
• [8] Kaczorek, T. (2007b). Realization problem for singular positive continuous-time systems with delays, Control and Cybernetics 36(1): 47-57.
• [9] Kaczorek, T. (2008). Fractional positive continuous-time linear systems and their reachability, International Journal of Applied Mathematics and Computer Science 18(2): 223-228, DOI:10.2478/v10006-008-0020-0.
• [10] Kaczorek, T. (2009). Selected Problems in the Theory of Fractional Systems, Białystok Technical University, Białystok, (in Polish).
• [11] Kaczorek, T. (2010). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(3): 453-458.
• [12] Kaczorek, T. (2011). Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica 3(1), (in press).
• [13] Kucera, V. and Zagalak, P. (1988). Fundamental theorem of state feedback for singular systems, Automatica 24(5): 653-658.
• [14] Podlubny I. (1999). Fractional Differential Equations, Academic Press, New York, NY.
• [15] Van Dooren, P. (1979). The computation of Kronecker's canonical form of a singular pencil, Linear Algebra and Its Applications 27(1): 103-140.