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2015 | 25 | 3 | 539-546
Tytuł artykułu

Analysis of the descriptor Roesser model with the use of the Drazin inverse

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A method of analysis for a class of descriptor 2D discrete-time linear systems described by the Roesser model with a regular pencil is proposed. The method is based on the transformation of the model to a special form with the use of elementary row and column operations and on the application of a Drazin inverse of matrices to handle the model. The method is illustrated with a numerical example.
Rocznik
Tom
25
Numer
3
Strony
539-546
Opis fizyczny
Daty
wydano
2015
otrzymano
2014-05-16
Twórcy
  • Faculty of Electrical Engineering, Białystok University of Technology, ul. Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
  • Bru, R., Coll, C., Romero-Vivo, S. and Sanchez, E. (2003). Some problems about structural properties of positive descriptor systems, in L. Benvenuti, A. de Santis and L. Farina (Eds.), Positive Systems, Lecture Notes in Control and Information Sciences, Vol. 294, Springer, Berlin, pp. 233-240.
  • Bru, R., Coll, C. and Sanchez, E. (2000). About positively discrete-time singular systems, in M.E. Mastorakis (Ed.), System and Control: Theory and Applications, World Scientific and Engineering Society, Athens, pp. 44-48.
  • Bru, R., Coll, C. and Sanchez, E. (2002). Structural properties of positive linear time-invariant difference-algebraic equations, Linear Algebra and Its Applications 349: 1-10.
  • Busłowicz, M. (2014). Controllability, reachability and minimum energy control of fractional discrete-time linear systems with multiple delays in state, Bulletin of the Polish Academy of Sciences: Technical Sciences 62(2): 233-239.
  • Campbell, S.L., Meyer, C.D. and Rose, N.J., (1976). Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients, SIAM Journal on Applied Mathematics 31(3): 411-425.
  • Dai, L. (1989). Singular Control Systems, Lectures Notes in Control and Information Sciences, Springer-Verlag, Berlin.
  • Dodig, M. and Stosic, M. (2009). Singular systems state feedbacks problems, Linear Algebra and Its Applications 431(8): 1267-1292.
  • Duan, G.-R. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY.
  • Fahmy, M.M, and O'Reill, J. (1989). Matrix pencil of closed-loop descriptor systems: Infinite-eigenvalues assignment, International Journal of Control 49(4): 1421-1431.
  • Gantmacher, F.R. (1960). The Theory of Matrices, Chelsea Publishing Co., New York, NY.
  • Kaczorek, T. (1992). Linear Control Systems, Vol. 1, Research Studies Press J. Wiley, New York, NY.
  • Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.
  • Kaczorek, T. (2004). Infinite eigenvalue assignment by an output feedback for singular systems, International Journal of Applied Mathematics and Computer Science 14(1): 19-23.
  • Kaczorek, T. (2010). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(3): 453-458.
  • Kaczorek, T. (2011a). Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm, Archives of Control Sciences 21(3): 287-298.
  • Kaczorek, T. (2011b). Reduction and decomposition of singular fractional discrete-time linear systems, Acta Mechanica et Automatica 5(4): 62-66.
  • Kaczorek T. (2011c). Singular fractional discrete-time linear systems, Control and Cybernetics 40(3): 753-761.
  • Kaczorek, T. (2011d). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
  • Kaczorek, T. (2013). Application of the Drazin inverse to analysis of descriptor fractional discrete-time linear systems with regular pencils, International Journal of Applied Mathematics and Computer Science 23(1): 29-33, doi: 10.2478/amcs-2013-0003.
  • Kaczorek, T. (2014a). Drazin inverse matrix method for fractional descriptor continuous-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 62(3): 409-412.
  • Kaczorek, T. (2014b). Minimum energy control of descriptor positive discrete-time linear systems, COMPEL 33(3): 1-14.
  • Kaczorek, T. (2014c). Minimum energy control of positive fractional descriptor continuous-time linear systems, IET Control Theory and Applications 8(4): 219-225.
  • Kucera, V. and Zagalak, P. (1988). Fundamental theorem of state feedback for singular systems, Automatica 24(5): 653-658.
  • Van Dooren, P. (1979). The computation of Kronecker's canonical form of a singular pencil, Linear Algebra and Its Applications 27: 103-140.
  • Virnik, E. (2008). Stability analysis of positive descriptor systems, Linear Algebra and Its Applications 429(10): 2640-2659.
Typ dokumentu
Bibliografia
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