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Positivity of descriptor linear systems with regular pencils

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Języki publikacji
EN
Abstrakty
EN
The positivity of descriptor continuous-time and discrete-time linear systems with regular pencils are addressed. Such systems can be reduced to standard linear systems and can be decomposed into dynamical and static parts. Two definitions of the positive systems are proposed. It is shown that the definitions are not equivalent. Conditions for the positivity of the systems and the relationship between two classes of positive systems are established. The considerations are illustrated by examples of electrical circuits and numerical examples.
Rocznik
Strony
101--113
Opis fizyczny
Bibliogr. 21 poz., rys.
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autor
Bibliografia
  • 1. Dodig M., Stosic M., Singular systems state feedbacks problems. Linear Algebra and its Applications 431(8): 1267-1292 (2009).
  • 2. Dai L., Singular Control Systems, Lectures Notes in Control and Information Sciences. Springer- Verlag, Berlin (1989).
  • 3. Fahmy M.H, O’Reill J., Matrix pencil of closed-loop descriptor systems: infinite-eigenvalues assignment. Int. J. Control 49(4): 1421-1431 (1989).
  • 4. Gantmacher F.R., The Theory of Matrices. Chelsea Publishing Co., New York (1960).
  • 5. Kaczorek T., Fractional positive continuous-time linear systems and their reachability. Int. J. Appl. Math. Comput. Sci. 18(2): 223-228 (2008).
  • 6. Kaczorek T., Infinite eigenvalue assignment by output-feedbacks for singular systems. Int. J. Appl. Math. Comput. Sci. 14(1): 19-23 (2004).
  • 7. Kaczorek T., Linear Control Systems. Vol. 1. Research Studies Press J. Wiley, New York (1992).
  • 8. Kaczorek T., Polynomial and Rational Matrices. Applications in Dynamical Systems Theory. Springer-Verlag, London (2007).
  • 9. Kaczorek T., Positive linear systems with different fractional orders. Bull. Pol. Ac. Sci. Techn. 58(3): 453-458 (2010).
  • 10. Kaczorek T., Realization problem for singular positive continuous-time systems with delays. Control and Cybernetics 36(1): 47-57 (2007).
  • 11. Kaczorek T., Selected Problems of Fractional Systems Theory. Springer-Verlag, Berlin (2011).
  • 12. Kaczorek T., Checking of the positivity of descriptor linear systems by the use of shuffle algorithm. Archives of Control Sciences (2012).
  • 13. Kaczorek T., Positivity and reachability of fractional electrical circuits. Acta Mechanica et Automatica 3(1): 42-54 (2011).
  • 14. Kaczorek T., Reduction and decomposition of singular fractional discrete-time linear systems. Acta Mechanica et Automatica 5(4) (2011).
  • 15. Kaczorek T., Singular fractional discrete-time linear systems. Control and Cybernetics 40(3) (2011).
  • 16. Kaczorek T., Singular fractional linear systems and electrical circuits. Int. J. Appl. Math. Comput. Sci. 21(2): 379-384 (2011).
  • 17. Kaczorek T., Positive 1D and 2D Systems. Springer-Verlag (2002).
  • 18. Kucera V., Zagalak P., Fundamental theorem of state feedback for singular systems. Automatica 24(5): 653-658 (1988).
  • 19. Luenberger D.G., Time-invariant descriptor systems. Automatica 14: 473-480 (1978).
  • 20. Podlubny I., Fractional Differential Equations. Academic Press, New York (1999).
  • 21. Van Dooren P., The computation of Kronecker’s canonical form of a singular pencil. Linear Algebra and Its Applications 27: 103-140 (1979).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPS4-0001-0038
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