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Fractional descriptor standard and positive discrete-time nonlinear systems

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Języki publikacji
EN
Abstrakty
EN
A method of analysis of the fractional descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on a numerical example.
Twórcy
autor
  • Faculty of Electrical Engineering, Bialystok University of Technology, 45D Wiejska St., 15-351 Bialystok, Poland
Bibliografia
  • [1] R. Bru, C. Coll, S. Romero-Vivo, and E. Sanchez, “Some problems about structural properties of positive descriptor systems”, Lecture Notes in Control and Inform. Sci. 294, 233–240 (2003).
  • [2] R. Bru, C. Coll, and E. Sanchez, “About positively discrete-time singular systems”, System and Control: Theory and Applications, Electr. Comput. Eng. Ser., World Sci. Eng. Soc. Press 1, 44–48 (2000).
  • [3] R. Bru, C. Coll, and E. Sanchez, “Structural properties of positive linear time-invariant difference-algebraic equations”, Linear Algebra and its Applications 349, 1–10 (2002).
  • [4] S.L. Campbell, C.D. Meyer, and N.J. Rose, “Applications of the Drazin inverse to linear systems of differential equations with singular constructions”, SIAMJ Appl. Math. 31 (3), 411–425 (1976).
  • [5] L. Dai, Singular Control Systems. Lectures Notes in Control and Information Sciences, Springer-Verlag, Berlin, 1989.
  • [6] M. Dodig and M. Stosic, “Singular systems state feedbacks problems”, Linear Algebra and Its Applications 431 (8), 1267–1292 (2009).
  • [7] M.M. Fahmy and J. O’Reill, “Matrix pencil of closed-loop descriptor systems: infinite-eigenvalues assignment”, Int. J. Control 49 (4), 1421–1431 (1989).
  • [8] D. Guang-Ren, Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010.
  • [9] 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), 29–34 (2013).
  • [10] T. Kaczorek, “Descriptor standard and positive discrete-time nonlinear systems”, in Automatization of Discrete Processes Theory and Applications, vol 1, pp. 113–126, Gliwice, 2014.
  • [11] T. Kaczorek, “Reduction and decomposition of singular fractional discrete-time linear systems”, Acta Mechanica et Automatica 5 (4), 62–66 (2011).
  • [12] T. Kaczorek, “Singular fractional discrete-time linear systems”, Control and Cybernetics 40 (3), 753–761 (2011).
  • [13] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin, 2011.
  • [14] T. Kaczorek, Linear Control Systems, vol. 1, Research Studies Press J. Wiley, New York, 1992.
  • [15] V. Kucera and P. Zagalak, “Fundamental theorem of state feedback for singular systems”, Automatica 24 (5), 653–658 (1988).
  • [16] P. Van Dooren, “The computation of Kronecker’s canonical form of a singular pencil”, Linear Algebra and Its Applications 27, 103–140 (1979).
  • [17] E. Virnik, “Stability analysis of positive descriptor systems”, Linear Algebra and Its Applications 429, 2640–2659 (2008).
  • [18] T. Kaczorek, “Infinite eigenvalue assignment by output-feedbacks for singular systems”, Int. J. Appl. Math. Comput. Sci. 14 (1), 19–23 (2004).
  • [19] T. Kaczorek, “Minimum energy control of descriptor positive discrete-time linear systems”, COMPEL, Int. J. Computation and Math. in Electrical and Electronic Engineering 33 (3), 976–988 (2014).
  • [20] T. Kaczorek, “Positive linear systems with different fractional orders”, Bull. Pol. Ac.: Tech. 58 (3), 453–458 (2010).
  • [21] T. Kaczorek, “Minimum energy control of positive fractional descriptor continuous-time linear systems”, Control Theory & Applications IET 8 (4), 215–225 (2014).
  • [22] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
  • [23] T. Kaczorek, “Drazin inverse matrix method for fractional descriptor continuous-time linear systems”, Bull. Pol. Ac.: Tech. 62 (2), 409–412 (2014).
  • [24] T. Kaczorek, “Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm”, Archives of Control Sciences 21 (3), 287–298 (2011).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0c5d7198-7a9d-4731-bf4f-44b4a64fdbb4
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