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2013 | 23 | 1 | 29-33
Tytuł artykułu

Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-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.
Rocznik
Tom
23
Numer
1
Strony
29-33
Opis fizyczny
Daty
wydano
2013
otrzymano
2012-04-25
poprawiono
2012-10-24
Twórcy
  • Faculty of Electrical Engineering, Białystok Technical University, 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. 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 N.E. Mastorakis (Ed.) System and Control: Theory and Applications, Electrical and Computer Engineering Series, 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 Applications 349(1-3): 1-10.
  • 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.
  • Commalut, C. and Marchand, N. (2006). Positive Systems, Lecture Notes in Control and Information Sciences, Vol. 341, Springer-Verlag, Berlin.
  • Dai, L. (1989). Singular Control Systems, Lectures Notes in Control and Information Sciences, Vol. 118, Springer-Verlag, Berlin.
  • Dodig, M. and Stosic, M. (2009). Singular systems state feedbacks problems, Linear Algebra and Its Applications 431(8): 1267-1292.
  • Fahmy, M.H, and O'Reill, J. (1989). Matrix pencil of closed-loop descriptor systems: Infinite-eigenvalues assignment, International Journal of Control 49(4): 1421-1431.
  • Farina, L. and Rinaldi, S. (2000). Positive Linear Systems, J. Willey, New York, NY.
  • 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. (2007a). Polynomial and Rational Matrices. Applications in Dynamical Systems Theory, Springer-Verlag, London.
  • Kaczorek, T. (2007b). Realization problem for singular positive continuous-time systems with delays, Control and Cybernetics 36(1): 47-57.
  • 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). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
  • Kaczorek T. (2011c). Singular fractional discrete-time linear systems, Control and Cybernetics 40(3): 1-8.
  • Kaczorek T. (2011d). Reduction and decomposition of singular fractional discrete-time linear systems, Acta Mechanica et Automatica 5(4): 1-5.
  • 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
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv23z1p29bwm
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