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Positivity of a class of fractional descriptor continuous-time nonlinear systems

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Języki publikacji
EN
Abstrakty
EN
The positivity of a class of fractional descriptor continuous-time nonlinear systems is addressed by the use of the Weierstrass- Kronecker decomposition of the pencil of linear part of nonlinear system. Sufficient conditions for the positivity are established and illustrated by an example of fractional continuous-time descriptor nonlinear systems.
Rocznik
Strony
561--565
Opis fizyczny
Bibliogr. 25 poz., rys., tab., wykr.
Twórcy
autor
  • Faculty of Electrical Engineering, Bialystok University of Technology, 45D Wiejska St., 15-351 Bialystok, Poland
Bibliografia
  • [1] L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
  • [2] T. Kaczorek, Positive 1D and 2D Systems, Springer Verlag, London, 2002.
  • [3] W. Mitkowski, “Dynamic properties of chain systems with applications to biological models”, Archives of Control Sciences 9 (XLV) (1-2), 123-131 (1999).
  • [4] 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. 294, 233-240.
  • [5] R. Bru, C. Coll, and E. Sanchez, “About positively discretetime singular systems, System and Control: theory and applications”, Electr. Comput. Eng. Ser., World Sci. Eng. Soc. Press 1, 44-48 (2000).
  • [6] R. Bru, C. Coll, and E. Sanchez, “Structural properties of positive linear time-invariant difference-algebraic equation”, Linear Algebra Appl. 349, 1-10 (2002).
  • [7] L. Dai, “Singular control systems”, in Lectures Notes in Control and Information Sciences, Springer-Verlag, Berlin, 1989.
  • [8] M. Dodig and M. Stosic, “Singular systems state feedbacks problems”, Linear Algebra and its Applications 431 (8), 1267-1292 (2009).
  • [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), 409-412 (2014).
  • [11] T. Kaczorek, “Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm”, Archives of Control Sciences 21, 287-298 (2011).
  • [12] T. Kaczorek, “Infinite eigenvalue assignment by outputfeedbacks for singular systems”, Int. J. Appl. Math. Comput. Sci. 14, 19-23 (2004).
  • [13] T. Kaczorek, Linear Control Systems, vol. 1, Research Studies Press J. Wiley, New York, 1992.
  • [14] W. Xiang-Jun, W. Zheng-Mao, and L. Jun-Guo, “Stability analysis of a class of nonlinear fractional-order systems”, IEEE Trans. Circuits and Systems-II, Express Briefs 55, 1178-1182 (2008).
  • [15] T. Kaczorek, “Positive linear systems with different fractional orders”, Bull. Pol. Ac.: Tech. 58 (3), 453-458 (2010).
  • [16] T. Kaczorek, Selected Problems of Fractional System Theory, Springer Verlag, Berlin, 2011.
  • [17] T. Kaczorek, “Positive linear systems consisting of n subsystems with different fractional orders”, IEEE Trans. on Circuits and Systems 58, 1203-1210 (2011).
  • [18] 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, 29-34 (2013).
  • [19] E. Virnik, “Stability analysis of positive descriptor systems”, Linear Algebra and its Applications 429, 2640-2659 (2008).
  • [20] M. Busłowicz, “Stability of linear continuous-time fractional order systems with delays of the retarded type”, Bull. Pol. Ac.: Tech. 56 (4), 319-324 (2008).
  • [21] M. Busłowicz, “Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders”, Bull. Pol. Ac.: Tech. 60 (2), 279-284 (2012).
  • [22] M. Busłowicz and T. Kaczorek, “Simple conditions for practical stability of positive fractional discrete-time linear systems”, Int. J. Appl. Math. Comput. Sci. 19, 263-169 (2009).
  • [23] T. Kaczorek, “Descriptor standard and positive discrete-time nonlinear systems”, Bull. Pol. Ac.: Tech. 63 (3), (2015), (to be published).
  • [24] W. Mitkowski, “Remarks on stability of positive linear systems”, Control and Cybernetics 29, 295-304 (2000).
  • [25] W. Mitkowski, “Dynamical properties of Metzler systems”, Bull. Pol. Ac.: Tech. 56 (4), 309-312 (2008).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b3c577fb-1ea0-453d-bc1f-17889ede2019
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