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Drazin inverse matrix method for fractional descriptor discrete-time linear systems

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EN
Abstrakty
EN
The Drazin inverse of matrices is applied in order to find the solutions of the state equations of fractional descriptor discrete-time linear systems. The solution of the state equation is derived and the set of consistent initial conditions for a given set of admissible inputs is established. The proposed method is illustrated by a numerical example.
Twórcy
autor
  • Faculty of Electrical Engineering Bialystok University of Technology, 45D Wiejska Sr., 15-351 Bialystok
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., vol. 294, Springer, Berlin, 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, Athens Algebra Appl., 349
  • [3] R. Bru, C. Coll, and E. Sanchez, “Structural properties of positive linear time-invariant difference-algebraic equations”, Linear Algebra Appl., 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 constant coefficients”, 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] F.R. Gantmacher, The theory of Matrices, Chelsea Publishing Co., New York, 1960.
  • [9] D. Guang-Ren, Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010.
  • [10] T. Kaczorek, “Drazin inverse matrix method for fractional descriptor continuous-time linear systems”, Bull. Pol. Ac.: Tech., 62 (3), 233‒239 (2014). [Web of Science]
  • [11] 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).
  • [12] T. Kaczorek, “Infinite eigenvalue assignment by output-feedbacks for singular systems”, Int. J. Appl. Math. Comput. Sci., 14 (1), 19‒23 (2004).
  • [13] 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).
  • [14] T. Kaczorek, “Reduction and decomposition of singular fractional discrete-time linear systems”, Acta Mechanica et Automatica, 5 (4), 62‒66 (2011).
  • [15] T. Kaczorek, “Singular fractional discrete-time linear systems”, Control and Cybernetics, 40 (3), 753‒761 (2011).
  • [16] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin, 2011.
  • [17] T. Kaczorek, Linear Control Systems, vol. 1, Research Studies Press J. Wiley, New York, 1992.
  • [18] V. Kucera and P. Zagalak, “Fundamental theorem of state feedback for singular systems”, Automatica, 24 (5), 653‒658 (1988).
  • [19] P. Van Dooren, “The computation of Kronecker’s canonical form of a singular pencil”, Linear Algebra and its Applications, 27, 103‒140 (1979).
  • [20] T. Kaczorek, “Minimum energy control of descriptor positive discrete-time linear systems”, COMPEL, 33 (3), 976‒988 (2014).
  • [21] T. Kaczorek, “Minimum energy control of positive fractional descriptor continuous-time linear systems”, IET Control Theory and Applications, 8 (4), 219‒225 (2013).
  • [22] T. Kaczorek, “Positive linear systems with different fractional orders”, Bull. Pol. Ac.: Tech., 58 (3), 453‒458 (2010).
  • [23] E. Virnik, “Stability analysis of positive descriptor systems”, Linear Algebra and its Applications, 429 (10), 2640‒2659 (2008).
  • [24] M. Busłowicz, “Controllability, reachability and minimum energy control of fractional discrete-time linear systems with multiple delays in state”, Bull. Pol. Ac.: Tech., 62 (2), 233‒239 (2014).
  • [25] Ł. Sajewski, “Descriptor fractional discrete-time linear system and its solution - comparison of three different methods”, Challenges in Automation, Robotics and Measurement Techniques, Advances in Intelligent Systems and Computing, 440, 37‒50 (2016).
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
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Bibliografia
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