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Descriptor standard and positive discrete-time nonlinear systems

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Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A method of analysis of 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 numerical examples.
Rocznik
Strony
227--235
Opis fizyczny
Bibliogr. 23 poz., wzory
Twórcy
autor
  • Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Bialystok
Bibliografia
  • [1] R. Bru, C. Coll, S. Romero-Vivo and E. Sanchez: Some problems about structural properties of positive descriptor systems. Positive systems, Lecture Notes in Control and Inform. Sci., Springer, Berlin, 294 2003, 233-240.
  • [2] B. Bru, C. C 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, 2000, 44-48.
  • [3] B. Bru, C. Coll and E. Sanchez: Structural properties of positive linear timeinvariant difference-algebraic equations. Linear Algebra and its Applications., 349 (2002), 1-10.
  • [4] S. L. Campbell, C. D. Meyer and N. J. Rose: Applications of the Drazin inverse tolinear systems of differential equations with singular constructions. SIAM J. on Applied Mathematics, 31(3), (1976), 411-425.
  • [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), (2009), 1267-1292.
  • [7] M. M. Fahmy and J. O’Reill: Matrix pencil of closed-loop descriptor systems: infinite-eigenvalues assignment. Int. J. Control, 49(4), (1989), 1421-1431.
  • [8] Duan Guang-Ren: Analysis and Design of Descriptor Linear Systems. Springer, New York, 2010.
  • [9] T. Kaczorek: Drazin inverse matrix method for fractional descriptor continuoustime linear systems. Bull. Pol. Acad.: Tech., 62(2), (2014).
  • [10] T. Kaczorek: Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm. Archives of Control Sciences, 21(3), (2011), 287-298.
  • [11] T. Kaczorek: Infinite eigenvalue assignment by output-feedbacks for singular systems. Int. J. Appl. Math. Comput. Sci., 14(1), (2004), 19-23.
  • [12] T. Kaczorek: Minimum energy control of descriptor positive discrete-time linear systems. COMPEL: The Int. J. for Computation and Mathematics in Electrical and Electronic Engineering, 33(3), (2014), 976-988.
  • [13] T. Kaczorek: Positive linear systems with different fractional orders. Bull. Pol. Ac. Sci. Techn., 58(3), (2010), 453-458.
  • [14] T. Kaczorek: Minimum energy control of positive fractional descriptor continuous-time linear systems. Control Theory & Applications IET, 8(4), (2014), 215-225.
  • [15] T. Kaczorek: Positive 1D and 2D Systems. Springer-Verlag, London, 2002.
  • [16] 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), (2013), 29-34.
  • [17] T. Kaczorek: Reduction and decomposition of singular fractional discrete-time linear systems. Acta Mechanica et Automatica, 5(4), (2011), 62-66.
  • [18] T. Kaczorek: Singular fractional discrete-time linear systems. Control and Cybernetics, 40(3), (2011), 753-761.
  • [19] T. Kaczorek: Selected Problems of Fractional Systems Theory. Springer-Verlag, Berlin, 2011.
  • [20] T. Kaczorek: Linear Control Systems. 1 Research Studies Press J. Wiley, New York, 1992.
  • [21] V. Kucera and P. Zagalak: Fundamental theorem of state feedback for singular systems. Automatica, 24(5), (1998), 653-658.
  • [22] P. Van Dooren: The computation of Kronecker’s canonical form of a singular pencil. Linear Algebra and its Applications, 27 (1979), 103-140.
  • [23] E. Virnik: Stability analysis of positive descriptor systems. Linear Algebra and its Applications, 429 (2008), 2640-2659.
Uwagi
EN
This work was supported by Ministry of Science and Higher Education in Poland under work S/WE/1/11
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6603cc11-f2ab-4438-b0bc-a9f58a092032
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