Descriptor fractional discrete-time linear system with two different fractional orders and its solution

• Autorzy: Sajewski Ł.

Identyfikatory

DOI

10.1515/bpasts-2016-0003

• Języki publikacji: EN

Abstrakty

EN

Factional Discrete-time linear systems with fractional different orders are addressed. The Weierstrass-Kronecker decomposition theorem of the regular pencil is extended to the descriptor fractional discrete-time linear system with different fractional orders. Using the extension, method for finding the solution of the state equation is derived. Effectiveness of the method is demonstrated on a numerical example.

Słowa kluczowe

EN

fractional; different order; descriptor; solution

PL

układ nieliniowy; deskryptor; rozwiązanie; systemy liniowe

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2016
• Tom: Vol. 64, nr 1
• Strony: 15--20
• Opis fizyczny: Bibliogr. 30 poz.

Twórcy

autor

Sajewski Ł.

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

Bibliografia

• [1] S.L. Campbell, C.D. Meyer, and N.J. Rose, “Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients”, SIAMJ Appl. Math. 31 (3), 411-425 (1976).
• [2] L. Dai, Singular Control Systems, Lectures Notes in Control and Information Sciences, Springer-Verlag, Berlin, 1989.
• [3] M. Dodig and M. Stosic, “Singular systems state feedbacks problems”, Linear Algebra and Its Applications 431 (8), 1267-1292 (2009).
• [4] D. Guang-Ren, Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010.
• [5] T. Kaczorek, “Descriptor fractional linear systems with regular pencils”, Int. J. Appl. Math. Comput. Sci. 23 (2), 309-315 (2013).
• [6] T. Kaczorek, “Singular fractional continuous-time and discretetime linear systems”, Acta Mechanica et Automatica 7 (1), 26-33 (2013).
• [7] T. Kaczorek, “Singular fractional discrete-time linear systems”, Control and Cybernetics 40 (3), 1-8 (2011).
• [8] P. Van Dooren, “The computation of Kronecker’s canonical form of a singular pencil”, Linear Algebra and Its Applications 27, 103-140 (1979).
• [9] P. Van Dooren and T. Beelen, “An improved algorithm for the computation of Kronecker’s canonical form of a singular pencil”, Linear Algebra and Its Applications 105, 9-65 (1988).
• [10] K. Nishimoto, Fractional Calculus, Decartess Press, Koriama, 1984.
• [11] K.B. Oldham and J. Spanier, The Fractional Calculus, Academmic Press, New York, 1974.
• [12] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
• [13] A. Dzieliński, D. Sierociuk, and G. Sarwas, “Ultracapacitor parameters identification based on fractional order model”, Proc. Eur. Control Conf. (ECC) 1, 196-200 (2009).
• [14] N.M.F. Ferreira and J.A.T Machado, “Fractional-order hybrid control of robotic manipulators”, Proc. 11th Int. Conf. Advanced Robotics, ICAR 1, 393-398 (2003).
• [15] J.K. Popović, S. Pilipović, and T.M. Atanacković, “Two compartmental fractional derivative model with fractional derivatives of different order”, Communications in Nonlinear Science and Numerical Simulation 18 (9), 2507-2514 (2013).
• [16] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differenctial Equations, Willey, New York, 1993.
• [17] T. Kaczorek, “Solution of the state equations of descriptor fractional discrete-time linear systems with regular pencils”, Tech. Transp. Szyn. 10, 415-422 (2013).
• [18] T. Kaczorek, “Reduction and decomposition of singular fractional discrete-time linear systems”, Acta Mechanica et Automatica 5 (4), 1-5 (2011).
• [19] T. Kaczorek, “Application of Drazin inverse to analysis of descriptor fractional discrete-time linear systems with regular pencils”, Int. J. Appl. Math. Comput. Sci. 23 (1), 29-33 (2013).
• [20] T. Kaczorek, “Drazin inverse matrix method for fractional descriptor continuous-time linear systems”, Bull. Pol. Ac.: Tech. 62 (3), 409-412, (2014).
• [21] T. Kaczorek, “Fractional positive linear systems”, Kybernetes: Int. J. Systems & Cybernetics 38 (7/8), 1059-1078 (2009).
• [22] T. Kazorek, Selected Problems in Fractional Systems Theory, Springer-Verlag, Berlin, 2011.
• [23] T. Kaczorek, “Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. Circuits and Systems 58 (6), 1203-1210 (2011).
• [24] T. Kaczorek, “Positive linear systems with different fractional orders, Bull. Pol. Ac.: Tech. 58 (3), 453-458 (2010).
• [25] M. Busłowicz, “Stability analysis of continuous-time linear systems consisting of n subsystem with different fractional orders”, Bull. Pol. Ac.: Tech. 60 (2), 279-284 (2012).
• [26] Ł. Sajewski, “Reachability, observability and minimum energy control of fractional positive continuous-time linear systems with two different fractional orders”, Multidim. Syst. Sign. Process. 25, DOI 10.1007/s11045-014-0287-2 (2014).
• [27] Ł. Sajewski, “Solution of the state equation of descriptor fractional continuous-time linear systems with two different fractional”, Progress in Automation, Robotics and Measuring Techniques, Advances in Intelligent Systems and Computing 350, 233-242 (2015).
• [28] Ł. Sajewski, “Descriptor fractional discrete-time linear system and its solution - comparison of three different methods”, Proc. Conf. Automation 1, (2016), (to be published).
• [29] T. Kaczorek, Vectors and Matrices in Automation and Electrotechnics, WNT, Warszawa, 1998.
• [30] T. Kaczorek, Linear Control Systems, vol. 1, Research Studies Press J. Wiley, New York, 1992.

Uwagi

PL

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