Descriptor fractional linear systems with regular pencils
Tadeusz Kaczorek
International Journal of Applied Mathematics and Computer Science, Tome 23 (2013), p. 309-315 / Harvested from The Polish Digital Mathematics Library
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Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:257114 
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     author = {Tadeusz Kaczorek},
     title = {Descriptor fractional linear systems with regular pencils},
     journal = {International Journal of Applied Mathematics and Computer Science},
     volume = {23},
     year = {2013},
     pages = {309-315},
     zbl = {1282.93136},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv23z2p309bwm}
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Tadeusz Kaczorek. Descriptor fractional linear systems with regular pencils. International Journal of Applied Mathematics and Computer Science, Tome 23 (2013) pp. 309-315. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv23z2p309bwm/

[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, Lectures Notes in Control and Information Sciences, Vol. 118, 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. (2012b). Positive fractional continuous-time linear systems with singular pencils, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(1): 9-12.

[005] Kaczorek, T. (2011a). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuits and Systems 58(7): 1203-1210.

[006] Kaczorek, T. (2011b). Selected Problems of Fractional System Theory, Springer-Verlag, Berlin. | Zbl 1221.93002

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

[008] Kaczorek, T. (2010b). Practical stability and asymptotic stability of positive fractional 2D linear systems, Asian Journal of Control 12(2): 200-207.

[009] Kaczorek, T. (2012a). Descriptor fractional linear systems with regular pencils, Asian Journal of Control 15(4): 1-14.

[010] 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

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

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

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

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

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

[016] Luenberger, D.G. (1978). Time-invariant descriptor systems, Automatica 14: 473-480. | Zbl 0398.93040

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

[018] Wang, C. (2012). New delay-dependent stability criteria for descriptor systems with interval time delay, Asian Journal of Control 14(1): 197-206. | Zbl 1282.93228

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

[020] Yan L., YangQuan C., Hyo-Sung A., (2011c). Fractional-order iterative learning control for fractional-order systems, Asian Journal of Control 13(1): 54-63. | Zbl 1248.93085