Determination of positive stable realizations for discrete-time linear systems

eng Artykuł w języku angielskim DOI:

wyślij Tadeusz Kaczorek Faculty of Electrical Engineering, Białystok University of Technology, Białystok, Poland

Pobierz Artykuł

Abstract

Sufficient conditions for the existence of positive stable realizations for given proper transfer matrices are established. Two methods are proposed for determination of the positive stable realizations for given proper transfer matrices. The effectives of the proposed procedures is demonstrated on numerical examples.

Keywords

determination, discrete-time, positive, stable

Wyznaczanie dodatnich stabilnych realizacji dla dyskretnych układów linearnych

Streszczenie

Podane zostaną warunki wystarczające istnienia stabilnej realizacji dodatniej dla danej właściwej macierzy transmitancji operatorowych. Przedstawione zostaną dwie metody wyznaczania stabilnej realizacji dodatniej dla zadanej macierzy transmitancji operatorowych. Efektywność proponowanych metod zilustrowana zostanie przykładami numerycznymi.

Słowa kluczowe

realizacja dodatnia, stabilny, układ dyskretny, wyznaczanie

Bibliografia

  1. L. Benvenuti and L. Farina: “A tutorial on the positive realization problem,” IEEE Trans. Autom. Control, vol. 49, no. 5, 2004, 651-664.
  2. L. Farina and S. Rinaldi S.: “Positive Linear Systems,” Theory and Applications, J. Wiley, New York, 2000.
  3. T. Kaczorek: “A realization problem for positive continuous-time linear systems with reduced numbers of delays,” Int. J. Appl. Math. Comp. Sci. 2006, Vol. 16, No. 3, pp. 325-331.
  4. T. Kaczorek: “Computation of realizations of discretetime cone systems,” Bull. Pol. Acad. Sci. Techn. vol. 54, no. 3, 2006, 347-350.
  5. T. Kaczorek: “Linear Control Systems,” vol. 1, Research Studies Press, J. Wiley, New York 1992.
  6. T. Kaczorek: “Positive 1D and 2D Systems,” Springer-Verlag, London, 2002.
  7. T. Kaczorek: “Polynomial and Rational Matrices,” Springer-Verlag, London, 2009.
  8. T. Kaczorek: “Realization problem for fractional continuous-time systems,” Archives of Control Sciences, vol. 18, no. 1, 2008, 43-58.
  9. T. Kaczorek: “Realization problem for positive 2D hybrid systems,” COMPEL, vol. 27, no. 3, 2008, 613-623.
  10. T. Kaczorek: “Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs,” Int. J. Appl. Math. Comp. Sci., vol. 16, no. 2, 2006, 101-106.
  11. T. Kaczorek: “Realization problem for positive discrete-time systems with delay,” System Science, vol. 30, no. 4, 2004, 117-130.
  12. T. Kaczorek: “Positive minimal realizations for singular discrete-time systems with delays in state and delays in control,” Bull. Pol. Acad. Sci. Techn., vol 53, no. 3, 2005, 293-298.
  13. T. Kaczorek: “Positive stable realizations with system Metzler matrices,” Proc. MMAR Conf., 22-25 Sept. 2011, Międzyzdroje, Poland.
  14. T. Kaczorek: “Computation of positive stable realizations for linear continuous-time systems,” Proc. 20th European Conf. Circuit Theory and Design, August 29 to 31, 2011, Linköping, Sweden.
  15. T. Kaczorek: “Selected Problems in Fractional Systems Theory,” Springer-Verlag 2011.
  16. U. Shaker and M. Dixon: “Generalized minimal realization of transfer-function matrices,” Int. J. Contr., vol. 25, no. 5, 1977, 785-803.