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Pointwise completeness and pointwise degeneracy of fractional descriptor continuous-time linear systems with regular pencils

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Abstrakty
EN
Pointwise completeness and pointwise degeneracy of the fractional descriptor continuous-time linear systems with regular pencils are addressed. Conditions for the pointwise completeness and pointwise degeneracy of the systems are established and illustrated by an 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, “Structural properties of positive linear time-invariant difference-algebraic equations”, Linear Algebra Appl. 349, 1-10 (2002).
  • [3] 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, 411-425 (1976).
  • [4] L. Dai, Singular Control Systems, Springer-Verlag, Berlin, 1989.
  • [5] Guang-Ren Duan, Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010.
  • [6] 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, 29-33 (2013).
  • [7] 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).
  • [8] T. Kaczorek, “Drazin inverse matrix method for fractional descriptor continuous-time linear systems”, Bull. Pol. Ac.: Tech. 62, 409-412 (2014).
  • [9] T. Kaczorek, “Infinite eigenvalue assignment by outputfeedbacks for singular systems”, Int. J. Appl. Math. Comput. Sci. 14, 19-23 (2004).
  • [10] T. Kaczorek, Linear Control Systems, vol. 1, Research Studies Press J. Wiley, New York, 1992.
  • [11] T. Kaczorek, “Minimum energy control of positive fractional descriptor continuous-time linear systems”, IET Control Theory and Applications, doi:10.1049/oet-cta.2013.0362, 1-7 (2013).
  • [12] T. Kaczorek, “Reduction and decomposition of singular fractional discrete-time linear systems”, Acta Mechanica et Automatica 5, 62-66 (2011).
  • [13] T. Kaczorek, “Singular fractional discrete-time linear systems”, Control and Cybernetics 40, 753-761 (2011).
  • [14] E. Virnik, “Stability analysis of positive descriptor systems”, Linear Algebra and Its Applications 429, 2640-2659 (2008).
  • [15] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin, 2011.
  • [16] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
  • [17] M. Busłowicz, “Pointwise completeness and pointwise degeneracy of linear discrete-time systems of fractional order”, Automatics. Notebooks of the Silesian University of Technology 151, 19-24 (2008), (in Polish).
  • [18] M. Busłowicz, R. Kociszewski, and W. Trzasko, “Pointwise completeness and pointwise degeneracy of positive discrete-time systems with delays”, Automatics. Notebooks of the Silesian University of Technology 145, 51-56 (2006), (in Polish).
  • [19] A.K. Choudhury, “Necessary and sufficient conditions of pointwise completeness of linear time-invariant delay-differential systems”, Int. J. Control 16, 1083-1100 (1972).
  • [20] T. Kaczorek and M. Busłowicz, “Pointwise completeness and pointwise degeneracy of linear continuous-time fractional order systems”, J. Automation, Mobile Robotics & Intelligent Systems 3, 8-11 (2009).
  • [21] T. Kaczorek, “Pointwise completeness and pointwise degeneracy of 2D standard and positive Fornasini-Marchesini models”, COMPEL 30, 656-670 (2011).
  • [22] T. Kaczorek, “Pointwise completeness and pointwise degeneracy of standard and positive fractional linear systems with statefeedbacks”, Archives of Control Sciences 19, 295-306 (2009).
  • [23] T. Kaczorek, “Pointwise completeness and pointwise degeneracy of standard and positive linear systems with statefeedbacks”, JAMRIS 4, 3-7 (2010).
  • [24] A. Olbrot, “On degeneracy and related problems for linear constant time-lag systems”, Ricerche di Automatica 3, 203-220 (1972).
  • [25] V.M. Popov, “Pointwise degeneracy of linear time-invariant delay-differential equations”, J. Diff. Equation 11, 541-561 (1972).
  • [26] W. Trzasko, M. Busłowicz, and T. Kaczorek, “Pointwise completeness of discrete-time cone-systems with delays”, Proc. EUROCON 1, 606-611 (2007).
  • [27] L. Weiss, “Controllability for various linear and nonlinear systems models”, Lecture Notes in Mathematics 144, Seminar on Differential Equations and Dynamic System II, 250-262 (1970).
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Bibliografia
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