A modified state variable diagram method for determination of positive realizations of linear continuous-time systems with delays

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

A new modified state variable diagram method is proposed for determination of positive realizations of linear continuous-time systems with delays in state and input vectors. Using the method, it is possible to find a positive realization with reduced numbers of delays for a given transfer matrix. Sufficient conditions for the existence of positive realizations of given proper transfer matrices are established. The proposed method is demonstrated on numerical examples.

Słowa kluczowe

EN

state diagram method; determination; linear; continuous time; delay; realization

PL

oznaczanie; liniowy układ ciągły; opóźnienie; realizacja dodatnia

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2012
• Tom: Vol. 22, no. 4
• Strony: 897--905
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Białystok Technical University, ul. Wiejska 45D, 15-351 Białystok, Poland,

Bibliografia

• [1] Benvenuti L. and Farina L. (2004). A tutorial on the positive realization problem, IEEE Transactions on Automatic Control 49(5): 651-664.
• [2] Farina L. and Rinaldi S. (2000). Positive Linear Systems, Theory and Applications, J. Wiley, New York, NY.
• [3] Kaczorek T. (1992). Linear Control Systems, Vol.1, Research Studies Press, J. Wiley, New York, NY.
• [4] Kaczorek T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.
• [5] Kaczorek T. (2004). Realization problem for positive discrete-time systems with delay, System Science 30(4): 117-130.
• [6] Kaczorek T. (2005). Positive minimal realizations for singular discrete-time systems with delays in state and delays in control, Bulletin of the Polish Academy of Sciences: Technical Sciences 53(3): 293-298.
• [7] Kaczorek T. (2006a). A realization problem for positive continuous-time linear systems with reduced numbers of delays, International Journal of Applied Mathematics and Computer Science 16(3): 325-331.
• [8] Kaczorek T. (2006b). Computation of realizations of discrete-time cone systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 54(3): 347-350.
• [9] Kaczorek T. (2006c). Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs, International Journal of Applied Mathematics and Computer Science 16(2): 169-174.
• [10] Kaczorek T. (2008a). Realization problem for fractional continuous-time systems, Archives of Control Sciences 18(1): 43-58.
• [11] Kaczorek T. (2008b). Realization problem for positive 2D hybrid systems, COMPEL 27(3): 613-623.
• [12] Kaczorek T. (2008c). Fractional positive continuous-time linear systems and their reachability, International Journal of Applied Mathematics and Computer Science 18(2): 223-228, DOI: 10.2478/v10006-008-0020-0.
• [13] Kaczorek T. (2009a). Fractional positive linear systems, Kybernetes: The International Journal of Systems & Cybernetics 38(7/8): 1059-1078.
• [14] Kaczorek T. (2009b). Polynomial and Rational Matrices, Springer-Verlag, London.
• [15] Kaczorek T. (2011a). Computation of positive stable realizations for linear continuous-time systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 59(3): 273-281 and Proceedings of the 20th European Conference on Circuit Theory and Design, Linköping, Sweden.
• [16] Kaczorek T. (2011b). Positive stable realizations of fractional continuous-time linear systems, International Journal of Applied Mathematics and Computer Science 21(4): 697-702, DOI: 10.2478/v10006-011-0055-5.
• [17] Kaczorek T. (2011c). Positive stable realizations with system Metzler matrices, Archives of Control Sciences 21(2): 167-188 and Proceedings of the MMAR'2011 Conference, Międzyzdroje, Poland, (on CD-ROM).
• [18] Kaczorek T. (2011d). Selected Problems in Fractional Systems Theory, Springer-Verlag, London.
• [19] Kaczorek T. (2012a). Existence and determination of the set of Metzler matrices for given stable polynomials, International Journal of Applied Mathematics and Computer Science 22(2): 389-399, DOI: 10.2478/v10006-012-0029-2.
• [20] Kaczorek T. (2012b). Positive stable realizations of discrete-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(3): 605-616.
• [21] Shaker U. and Dixon M. (1977). Generalized minimal realization of transfer-function matrices, International Journal of Control 25(5): 785-803.