Singular fractional linear systems and electrical circuits
Tadeusz Kaczorek
International Journal of Applied Mathematics and Computer Science, Tome 21 (2011), p. 379-384 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:208054 
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     title = {Singular fractional linear systems and electrical circuits},
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     year = {2011},
     pages = {379-384},
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Tadeusz Kaczorek. Singular fractional linear systems and electrical circuits. International Journal of Applied Mathematics and Computer Science, Tome 21 (2011) pp. 379-384. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv21i2p379bwm/

[000] Dodig, M. and Stosic, M. (2009). Singular systems state feedbacks problems, Linear Algebra and Its Applications 431(8): 1267-1292. | Zbl 1170.93016

[001] Dai, L. (1989). Singular Control Systems, Springer-Verlag, Berlin. | Zbl 0669.93034

[002] 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. | Zbl 0681.93036

[003] Gantmacher, F.R. (1960). The Theory of Matrices, Chelsea Publishing Co., New York, NY. | Zbl 0088.25103

[004] Kaczorek, T. (1992). Linear Control Systems, Vol. 1, Research Studies Press, John Wiley, New York, NY. | Zbl 0784.93002

[005] Kaczorek, T. (2004). Infinite eigenvalue assignment by outputfeedbacks for singular systems, International Journal of Applied Mathematics and Computer Science 14(1): 19-23. | Zbl 1171.93331

[006] Kaczorek, T. (2007a). Polynomial and Rational Matrices. Applications in Dynamical Systems Theory, Springer-Verlag, London. | Zbl 1114.15019

[007] Kaczorek, T. (2007b). Realization problem for singular positive continuous-time systems with delays, Control and Cybernetics 36(1): 47-57. | Zbl 1293.93378

[008] 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. | Zbl 1235.34019

[009] Kaczorek, T. (2009). Selected Problems in the Theory of Fractional Systems, Białystok Technical University, Białystok, (in Polish).

[010] Kaczorek, T. (2010). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(3): 453-458. | Zbl 1220.78074

[011] Kaczorek, T. (2011). Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica 3(1), (in press).

[012] Kucera, V. and Zagalak, P. (1988). Fundamental theorem of state feedback for singular systems, Automatica 24(5): 653-658. | Zbl 0661.93033

[013] Podlubny I. (1999). Fractional Differential Equations, Academic Press, New York, NY. | Zbl 0924.34008

[014] Van Dooren, P. (1979). The computation of Kronecker's canonical form of a singular pencil, Linear Algebra and Its Applications 27(1): 103-140. | Zbl 0416.65026