Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

A new modified state variable diagram method is proposed for determination of positive realizations with reduced numbers of delays and without delays of linear discrete-time systems for a given transfer function. Sufficient conditions for the existence of the positive realizations of given proper transfer function are established. It is shown that there exists a positive realization with reduced numbers of delays if there exists a positive realization without delays but with greater dimension. The proposed methods are demonstrated on a numerical example.

Słowa kluczowe

EN

state diagram method; determination; linear; discrete-time; delay; realization

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2012
• Tom: Vol. 22, no. 4
• Strony: 451--465
• Opis fizyczny: Bibliogr. 23 poz., rys., tab.

Twórcy

autor

Kaczorek T.

• Bialystok University of Technology, Faculty of Electrical Engineering, 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. on Automatic Control, 49(5), (2004), 651-664.
• [4] T. Kaczorek: A realization problem for positive continuous-time linear systems with reduced numbers of delays. Int. J. Appl. Math. Comp. Sci., 16(3), (2006), 325-331.
• [5] T. Kaczorek: Computation of realizations of discrete-time cone systems. Bull. Pol. Acad. Sci. Techn., 54(3), (2006), 347-350.
• [6] T. Kaczorek: Computation of positive stable realization for linear continuoustime systems. Bull. Pol. Acad. Sci. Techn., 59(3), (2011), 273-281 and Proc. of20th European Conf. Circuit Theory and Design, (2011), Linköping, Sweden.
• [7] T. Kaczorek: Positive stable realizations of fractional continuous-time linear systems. Int. J. Appl. Math. Comp. Sci., 21(4), (2011), 697-702.
• [8] 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), (2006), 101-106.
• [9] T. Kaczorek: Realization problem for positive discrete-time systems with delays. System Science, 30(4), (2004), 117-130.
• [10] T. Kaczorek: Positive minimal realizations for singular discrete-time systems with delays in state and delays in control. Bull. Pol. Acad. Sci. Techn., 53(3), (2005), 293-298.
• [11] T. Kaczorek: Realization problem for fractional continuous-time systems. Archives of Control Sciences, 18(1), (2008), 43-58.
• [12] T. Kaczorek: Positive stable realizations with system Metzler matrices. Archivesof Control Sciences, 21(2), (2011), 167-188 and Proc. MMAR Conf., (2011), Miedzyzdroje, Poland.
• [13] T. Kaczorek: Realization problem for positive 2D hybrid systems. COMPEL, 27(3), (2008), 613-623.
• [14] T. Kaczorek: Fractional positive continuous-time linear systems and their reachability. Int. J. Appl. Math. Comp. Sci., 18(2), (2008), 223-228.
• [15] T. Kaczorek: Fractional positive linear systems. Kybernetes: The InternationalJournal of Systems and Cybernetics, 38(7/8), (2009), 1059-1078.
• [16] T. Kaczorek: Linear Control Systems. 1 Research Studies Press, J. Wiley, New York 1992.
• [17] T. Kaczorek: Polynomial and Rational Matrices. Springer-Verlag, London, 2009.
• [18] T. Kaczorek: Selected Problems in Fractional Systems Theory. Springer-Verlag, 2011.
• [19] T. Kaczorek: Existence and determination of the set of Metzler matrices for given stable polynomials. Int. J. Appl. Comput. Sci., 22(2), (2012), 389-399.
• [20] T. Kaczorek: Positive stable realizations of continuous-time linear systems. Proc. Conf. Int. Inf. and Eng. Syst., Krynica-Zdrój, (2012), Poland.
• [21] T. Kaczorek: Positive stable realizations of discrete-time linear systems. Archiveof Control Sciences, 22(2), (2012), 145-159.
• [22] T. Kaczorek: Modified state variable diagram method for determination of positive realizations of linear continuous-time systems with delays. Int. J. Appl. Math. Comp. Sci., 22(4), (2012), (in Press).
• [23] U. Shaker and M. Dixon: Generalized minimal realization of transfer-function matrices. Int. J. Contr., 25(5), (1977), 785-803.