A new approach to the realization problem for fractional discrete-time linear systems

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.1515/bpasts-2016-0002

• Języki publikacji: EN

Abstrakty

EN

A new approach to the realization problem for fractional discrete-time linear systems is proposed. A procedure for computation of fractional realizations of given transfer matrices is presented and illustrated by numerical examples.

Słowa kluczowe

EN

fractional system; linear system; discrete-time system; computation procedure; realization; transfer matrix

PL

macierz transferu; system liniowy; procedura obliczeniowa; sterowanie

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2016
• Tom: Vol. 64, nr 1
• Strony: 9--14
• Opis fizyczny: Bibliogr. 35 poz., rys.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• [1] L. Benvenuti and L. Farina, “A tutorial on the positive realization problem”, IEEE Trans. on Automatic Control 49 (5), 651-664 (2004).
• [2] L. Farina and S. Rinaldi, Positive Linear Systems. Theory and Applications, J. Wiley, New York, 2000.
• [3] T. Kaczorek, “Existence and determination of the set of Metzler matrices for given stable polynomials”, Int. J. Appl. Math. Comput. Sci. 22 (2), 389-399 (2012).
• [4] T. Kaczorek, Linear Control Systems, vol. 1, Research Studies Press, J. Wiley, New York, 1992.
• [5] T. Kaczorek, Polynomial and Rational Matrices, Springer, London, 2009.
• [6] T. Kaczorek and Ł. Sajewski, The Realization Problem for Positive and Fractional Systems, Springer, London, 2014.
• [7] T. Kaczorek, Selected Problems in Fractional Systems Theory, Springer, London, 2011.
• [8] U. Shaker and M. Dixon, “Generalized minimal realization of transfer-function matrices”, Int. J. Contr. 25 (5), 785-803 (1977).
• [9] T. Kaczorek, Positive 1D and 2D Systems, Springer, London, 2002.
• [10] T. Kaczorek, “A realization problem for positive continuoustime linear systems with reduced numbers of delays”, Int. J. Appl. Math. Comput. Sci. 16 (3), 325-331 (2006).
• [11] T. Kaczorek, “Computation of positive stable realizations for discrete-time linear systems”, Computational Problems of Electrical Engineering 2 (1), 41-48 (2012).
• [12] T. Kaczorek, “Computation of positive stable realizations for linear continuous-time systems”, Bull. Pol. Ac.: Tech. 59 (3), 273-281 (2011).
• [13] T. Kaczorek, “Computation of realizations of discrete-time cone systems”, Bull. Pol. Ac.: Tech. 54 (3), 347-350 (2006).
• [14] T. Kaczorek, “Positive and asymptotically stable realizations for descriptor discrete-time linear systems”, Bull. Pol. Ac.: Tech. 61 (1), 229-237 (2013).
• [15] 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).
• [16] T. Kaczorek, “Positive realizations for descriptor continuoustime linear systems”, Measurement Automation and Monitoring 56 (9), 815-818 (2012).
• [17] T. Kaczorek, “Positive realizations for descriptor discrete-time linear systems”, Acta Mechanica et Automatica, 6 (2), 58-61 (2012).
• [18] T. Kaczorek, “Positive stable realizations of continuous-time linear systems”, Proc. Conf. Int. Inf. and Eng. Syst. 1, CDROM (2012).
• [19] T. Kaczorek, “Positive stable realizations of discrete-time linear systems”, Bull. Pol. Ac.: Tech. 60 (3), 605-616 (2012).
• [20] T. Kaczorek, “Positive stable realizations with system Metzler matrices”, Archives of Control Sciences 21 (2), 167-188 (2011).
• [21] T. Kaczorek, “Realization problem for positive discretetime systems with delays”, System Science 30 (4), 117-130 (2004).
• [22] T. Kaczorek, “Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs”, Int. J. Appl. Math. Comput. Sci. 16 (2), 101-106 (2006).
• [23] T. Kaczorek, “Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems”, Archives of Control Sciences 22 (4), 371-384 (2012).
• [24] T. Kaczorek, “Positive realizations with reduced numbers of delays for 2-D continuous-discrete linear systems”, Bull. Pol. Ac.: Tech. 60 (4), 835-840 (2012).
• [25] T. Kaczorek, “Positive stable realizations for fractional descriptor continuous-time linear systems”, Archives of Control Sciences 22 (3), 255-265 (2012).
• [26] T. Kaczorek, “Positive stable realizations of fractional continuous-time linear systems”, Int. J. Appl. Math. Comput. Sci. 21 (4), 697-702 (2011).
• [27] T. Kaczorek, “Realization problem for descriptor positive fractional continuous-time linear systems”, Theory and Applications of Non-integer Order Systems, eds. W. Mitkowski, pp. 3-13, Springer, London, 2013.
• [28] T. Kaczorek, “Realization problem for fractional continuoustime systems”, Archives of Control Sciences 18 (1), 43-58 (2008).
• [29] Ł. Sajewski, “Positive stable minimal realization of fractional discrete-time linear systems”, Advances in the Theory and Applications of Non-integer Order Systems eds. W. Mitkowski, pp. 257, 15-30, Springer, London, 2013.
• [30] Ł. Sajewski, “Positive stable realization of fractional discretetime linear systems”, Asian J. Control 16 (3), DOI: 10.1002/asjc.750 (2014).
• [31] T. Kaczorek, “Positive realizations of hybrid linear systems described by the general model using state variable diagram method”, J. Automation, Mobile Robotics and Intelligent Systems 4, 3-10 (2010).
• [32] T. Kaczorek, “Realization problem for positive 2D hybrid systems”, COMPEL 27 (3), 613-623 (2008).
• [33] Ł. Sajewski, “Positive realization of fractional continuous-time linear systems with delays”, Measurement Automation and Monitoring 58 (5), 413-417 (2012).
• [34] Ł. Sajewski, “Positive realization of fractional discrete-time linear systems with delays”, Measurements, Automatics, Robotics 2, CD-ROM, (2012).
• [35] T. Kaczorek, “A modified state variables diagram method for determination of positive realizations of linear continuoustime systems with delays”, Int. J. Appl. Math. Comput. Sci. 22 (4), 897-905 (2012).

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.