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2017 | 27 | 1 | 33-41
Tytuł artykułu

Minimum energy control of descriptor fractional discrete-time linear systems with two different fractional orders

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Reachability and minimum energy control of descriptor fractional discrete-time linear systems with different fractional orders are addressed. Using the Weierstrass-Kronecker decomposition theorem of the regular pencil, a solution to the state equation of descriptor fractional discrete-time linear systems with different fractional orders is given. The reachability condition of this class of systems is presented and used for solving the minimum energy control problem. The discussion is illustrated with numerical examples.
Rocznik
Tom
27
Numer
1
Strony
33-41
Opis fizyczny
Daty
wydano
2017
otrzymano
2016-04-19
poprawiono
2016-09-11
zaakceptowano
2016-12-10
Twórcy
  • Faculty of Electrical Engineering, Białystok University of Technology, ul. Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
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  • Kaczorek, T, and Klamka, J. (1986). Minimum energy control of 2D linear systems with variable coefficients, International Journal of Control 44(3): 645-650.
  • Kaczorek, T. (1998). Vectors and Matrices in Automation and Electrotechnics, WNT, Warsaw.
  • Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London, DOI: 10.1007/978-1-44710221-2.
  • Kaczorek, T. (2010). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(3): 453-458, DOI: 10.2478/v10175-010-0043-1.
  • Kaczorek, T. (2011a). Selected Problems in Fractional Systems Theory, Springer-Verlag, Berlin, DOI: 10.1007/978-3-642-20502-6.
  • Kaczorek, T. (2011b). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions Circuits and Systems 58(6): 1203-1210, DOI: 10.1109/TCSI.2010.2096111.
  • Kaczorek, T. (2011c). Reduction and decomposition of singular fractional discrete-time linear systems, Acta Mechanica et Automatica 5(5): 1-5.
  • Kaczorek, T. (2011d). Singular fractional discrete-time linear systems, Control and Cybernetics 40(3): 1-8.
  • Kaczorek, T. (2013a). Descriptor fractional linear systems with regular pencils, International Journal Applied Mathematics and Computer Science 23(2): 309-315, DOI: 10.2478/amcs-2013-0023.
  • Kaczorek, T. (2013b). Solution of the state equations of descriptor fractional discrete-time linear systems with regular pencils, Technika Transportu Szynowego 10: 415-422.
  • Kaczorek, T. (2013c). Singular fractional continuous-time and discrete-time linear systems, Acta Mechanica et Automatica 7(1): 26-33, DOI: 10.2478/ama-2013-0005.
  • Kaczorek, T. (2014). Minimum energy control of fractional descriptor positive discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 24(4): 735-743, DOI: 10.2478/amcs-2014-0054.
  • Klamka, J. (1991).Controllability of Dynamical Systems, Kluwer Academic Press, Dordrecht.
  • Klamka, J. (2009). Controllability and minimum energy control problem of infinite dimensional fractional discrete-time systems with delays, 1st Asian Conference on Intelligent Information and Database Systems ACIIDS, Dong Hoi, Vietnam, DOI: 10.1109/ACIIDS.2009.53.
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  • Klamka, J. (2014). Controllability and minimum energy control of linear fractional discrete-time infinite-dimensional systems, 11th IEEE International Conference on Control & Automation ICCA, Taichung, Taiwan, pp. 1210-1214, DOI: 10.1109/ICCA.2014.6871094.
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  • Sajewski, Ł. (2015). Solution of the state equation of descriptor fractional continuous-time linear systems with two different fractional, in R. Szewczyk et al. (Eds.), Progress in Automation, Robotics and Measuring Techniques, Advances in Intelligent Systems and Computing, Vol. 350, Springer, Cham, pp. 233-242, DOI: 10.1007/978-3-319-15796-2_24.
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  • Sajewski, Ł. (2016c). Descriptor fractional discrete-time linear system with two different fractional orders and its solution, Bulletin of the Polish Academy of Sciences: Technical Sciences 64(1): 15-20, DOI: 10.1515/bpasts-2016-0003.
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Typ dokumentu
Bibliografia
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