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

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Abstrakty
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The Drazin inverse of matrices is applied to find the solutions of the state equations of the fractional descriptor continuous-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.
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  • Faculty of Electrical Engineering, Bialystok University of Technology, 45D Wiejska St., 15-351 Bialystok, Poland, kaczorek@isep.pw.edu.pl
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 discretetime singular systems”, System and Control: Theory and Applications 15, 44-48 (2000).
  • [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] D. Guang-Ren, Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010.
  • [9] 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).
  • [10] T. Kaczorek, “Infinite eigenvalue assignment by outputfeedbacks for singular systems”, Int. J. Appl. Math. Comput. Sci. 14 (1), 19-23 (2004).
  • [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, Linear Control Systems, vol. 1, Research Studies Press J. Wiley, New York, 1992.
  • [14] P. Van Dooren, “The computation of Kronecker’s canonical form of a singular pencil”, Linear Algebra and Its Applications 27, 103-140 (1979).
  • [15] R. Virnik, “Stability analysis of positive descriptor systems”, Linear Algebra and its Applications 429, 2640-2659 (2008).
  • [16] F.R. Gantmacher, The Theory of Matrices, Chelsea Publishing Co., New York, 1960.
  • [17] V. Kucera and P. Zagalak, “Fundamental theorem of state feedback for singular systems”, Automatica 24 (5), 653-658 (1988).
  • [18] T. Kaczorek, “Minimum energy control of descriptor positive discrete-time linear systems, Compel 23 (2), 205-211 (2013).
  • [19] T. Kaczorek, “Minimum energy control of positive fractional descriptor continuous-time linear systems”, IET Control Theory and Applications 362, doi:10.1049/oet-cta.2013.0362, 1-7 (2013).
  • [20] T. Kaczorek, “Positive linear systems with different fractional orders”, Bull. Pol. Ac.: Tech. 58 (3), 453-458 (2010).
  • [21] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin, 2011.
  • [22] T. Kaczorek, Polynomial and Rational Matrices. Applications in Dynamical Systems Theory, Springer-Verlag, London, 2007.
  • [23] 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).
  • [24] C. Commalut and N. Marchand, “Positive systems”, Lecture Notes in Control and Inform. Sci. 341, CD-ROM (2006).
  • [25] L. Farina and S. Rinaldi, Positive Linear Systems, J. Willey, New York, 2000.
  • [26] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-e7cf6050-cdca-4f91-8253-09ed3b089dba
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