Positive realizations with reduced numbers of delays for 2D continuous-discrete linear systems

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

A new method is proposed for determination of positive realizations with reduced numbers of delays of linear 2D continuousdiscrete systems. Sufficient conditions for the existence of the positive realizations of a 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 a greater dimension. The proposed method is demonstrated on a numerical example.

Słowa kluczowe

EN

computation; linear; 2D continuous-discrete; delay; state-space realization; sufficient conditions

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2012
• Tom: Vol. 60, nr 4
• Strony: 835--840
• Opis fizyczny: Bibliogr. 24 poz., rys., tab.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• [1] L. Farina and S. Rinaldi, Positive Linear Systems, Theory andApplications, J. Wiley, New York, 2000.
• [2] L. Benvenuti and L. Farina, “A tutorial on the positive realization problem”, IEEE Trans. Autom. Control 49 (5), 651-664 (2004).
• [3] T. Kaczorek, “Positive stable realizations of discrete-time linear systems”, Archive of Control Sciences 22 (2), 303-313 (2012).
• [4] T. Kaczorek, „Positive stable realizations of fractional continuous-time linear systems”, Int. J. Appl. Math. Comp. Sci. 21 (4), 697-702 (2011).
• [5] T. Kaczorek, “Positive stable realizations with system Metzler matrices”, Archives of Control Sciences 21 (2), 167-188 (2011).
• [6] T. Kaczorek, “Reachability and minimum energy control of positive 2D continuous-discrete systems”, Bull. Pol. Ac.: Tech. 46 (1), 85-93 (1998).
• [7] T. Kaczorek, “Realization problem for fractional continuoustime systems”, Archives of Control Sciences 18 (1), 43-58 (2008).
• [8] T. Kaczorek, “Realization problem for positive 2D hybrid systems”, COMPEL 27 (3), 613-623 (2008).
• [9] T. Kaczorek, “Realization problem for positive discrete-time systems with delays”, System Science 30 (4), 117-130 (2004).
• [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. 16 (2), 101-106 (2006).
• [11] T. Kaczorek, Selected Problems in Fractional Systems Theory, Springer-Verlag, London, 2011.
• [12] U. Shaker and M. Dixon, “Generalized minimal realization of transfer-function matrices”, Int. J. Contr. 25 (5), 785-803 (1977).
• [13] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
• [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, “A realization problem for positive continuoustime linear systems with reduced numbers of delays”, Int. J. Appl. Math. Comp. Sci. 16 (3), 325-331 (2006).
• [17] T. Kaczorek, “Computation of positive stable realizations for linear continuous-time systems”, Bull. Pol. Ac.: Tech. 59 (3), 273-281 (2011).
• [18] T. Kaczorek, “Existence and determination of the set of Metzler matrices for given stable polynomials”, Int. J. Appl. Comput. Sci. 22 (2), 389-399 (2012).
• [19] T. Kaczorek, “Positive stable realizations of continuous-time linear systems”, Proc. Conf. Int. Inf. and Eng. Syst. 1, CDROM (2012).
• [20] 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).
• [21] T. Kaczorek, “Fractional positive continuous-time linear systems and their reachability”, Int. J. Appl. Math. Comput. Sci. 18 (2), 223-228 (2008).
• [22] T. Kaczorek, “Fractional positive linear systems”, Kybernetes:Int. J. Systems & Cybernetics 38 (7/8), 1059-1078 (2009).
• [23] 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), to be published.
• [24] T. Kaczorek, “Determination of positive realizations with reduced numbers of delays of without delays for discrete-time linear systems”, Archive of Control Sciences, 22 (4), (2012), to be published