Computation of positive stable realizations for linear continuous-time systems

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

Conditions for the existence of positive stable realizations with system Metzler matrices for proper transfer function are established. It is shown that there exists a proper stable realization of transfer function of second order if and only if the transfer function has real negative poles. Sufficient conditions for the existence of positive stable realizations of transfer function of third order are established. A method based on the decomposition of transfer functions into the first, second and third orders transfer functions for computation of positive stable realizations is proposed. A method for computation of positive stable realizations of transfer functions with real negative poles and zeros is given.

Słowa kluczowe

EN

positive; stable; realization; system Metzler matrix; procedure; linear continuous-time

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2011
• Tom: Vol. 59, nr 3
• Strony: 273--281
• Opis fizyczny: Bibliogr. 17 poz., rys., tab.

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Bialystok University of Technology, 45D Wiejska St., 15-351 Bialystok, Poland,

Bibliografia

• [1] L. Farina and S. Rinaldi, Positive Linear Systems, Theory and Applications, J. Wiley, New York, 2000.
• [2] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
• [3] L. Benvenuti and L. Farina, “A tutorial on the positive realization problem”, IEEE Trans. Autom. Control 49 (5), 651–664 (2004).
• [4] T. Kaczorek, “A realization problem for positive continuoustime linear systems with reduced numbers of delays”, Int. J. Appl. Math. Comp. Sci. 16 (3), 325–331 (2006).
• [5] T. Kaczorek, “Computation of realizations of discrete-time cone systems”, Bull. Pol. Ac.: Tech. 54 (3), 347–350 (2006).
• [6] 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. 16 (2), 101–106 (2006).
• [7] T. Kaczorek, “Realization problem for positive discrete-time systems with delay”, System Science 30 (4), 117–130 (2004).
• [8] T. Kaczorek, “Positive minimal realizations for singular discrete-time systems with delays in state and delays in control”, Bull. Pol. Ac.: Tech. 53 (3), 293–298 (2005).
• [9] T. Kaczorek, “Realization problem for fractional continuoustime systems”, Archives of Control Sciences 18 (1), 43-58 (2008).
• [10] T. Kaczorek, “Positive stable realizations with system Metzler matrices”, Proc. Conf. MMAR’11 1, CD-ROM (2011).
• [11] T. Kaczorek, “Realization problem for positive 2D hybrid systems”, COMPEL 27 (3), 613–623 (2008).
• [12] T. Kaczorek, “Fractional positive continuous-time linear systems and their reachability”, Int. J. Appl. Math. Comput. Sci. 18 (2), 223–228 (2008).
• [13] T. Kaczorek, “Fractional positive linear systems”, Kybernetes: Int. J. Systems & Cybernetics 38 (7/8), 1059–1078 (2009).
• [14] T. Kaczorek, Linear Control Systems, vol. 1, Research Studies Press, J. Wiley, New York, 1992.
• [15] T. Kaczorek, Polynomial and Rational Matrices, Springer-Verlag, London, 2009.
• [16] T. Kaczorek, Selected Problems in Fractional Systems Theory,Springer-Verlag, London, 2011.
• [17] U. Shaker and M. Dixon, “Generalized minimal realization of transfer-function matrices”, Int. J. Contr. 25 (5), 785–803 (1977).