Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
A new method for computation of positive realizations of given transfer matrices of fractional linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.
Czasopismo
Rocznik
Tom
Strony
511--525
Opis fizyczny
Bibliogr. 36 poz., wzory
Twórcy
autor
- Białystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
- [1] L. Benvenuti and L. Farina: A tutorial on the positive realization problem, IEEE Trans. on Automatic Control., 49(5) (2004), 651-664.
- [2] A. Berman and R. J. Plemmons: Nonnegative Matrices in the Mathematical Sciences, SIAM, 1994.
- [3] M. Busłowicz: Stability of linear continuous-time fractional order systems with delays of the retarded type, Bull. Pol. Acad. Sci. Tech., 56(4) (2008), 319- 324.
- [4] M. Busłowicz: Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders, Bull. Pol. Acad. Sci. Tech., 60(2) (2012), 279-284.
- [5] M. Busłowicz and T. Kaczmarek: Simple conditions for practical stability of positive fractional discrete-time linear systems, Int. J. Appl. Math. Comput. Sci., 19(2) (2009), 263-269.
- [6] L. Farina and S. Rinaldi: Positive Linear Systems. Theory and Applications, J. Wiley, New York, 2000.
- [7] T. Kaczorek: A modified state variable diagram method for determination of positive realizations of linear continuous-time systems with delays, Int. J. Appl. Math. Comput. Sci., 22(4) (2012), 897-905.
- [8] T. Kaczorek: A new method for determination of positive realizations of linear continuous-time systems, 2017.
- [9] T. Kaczorek: A new method for computation of positive realizations of linear discrete-time systems, Submitted to Bull. Pol. Acad. Sci. Tech., 2017.
- [10] T. Kaczorek: Analysis of positivity and stability of fractional discretetime nonlinear systems, Bull. Pol. Acad. Sci. Tech., 64(3) (2016), 491-494.
- [11] T. Kaczorek: A realization problem for positive continuous-time linear systems with reduced numbers of delays, Int. J. Appl. Math. Comput. Sci., 16(3) (2006), 325-331.
- [12] T. Kaczorek: Computation of positive stable realizations for linear continuous-time systems, Bull. Pol. Acad. Techn. Sci., 59(3) (2011), 273-281.
- [13] T. Kaczorek: Computation of realizations of discrete-time cone systems, Bull. Pol. Acad. Sci. Techn., 54(3) (2006), 347-350.
- [14] T. Kaczorek: Existence and determination of the set of Metzler matrices for given stable polynomials, Int. J. Appl.Math. Comput. Sci., 22(2) (2012), 389-399.
- [15] T. Kaczorek: Linear Control Systems: Analysis of Multivariable Systems, J. Wiley & Sons, New York, 1992.
- [16] T. Kaczorek: Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
- [17] T. Kaczorek: Positive linear systems with different fractional orders, Bull. Pol. Acad. Sci. Tech., 58(3) (2010), 453-458.
- [18] T. Kaczorek: Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. Circuits and Systems, 58(7) (2011), 1203-1210.
- [19] T. Kaczorek: Positive fractional continuous-time linear systems with singular pencils, Bull. Pol. Acad. Sci. Tech., 60(1) (2012), 9-12.
- [20] T. Kaczorek: Positive minimal realizations for singular discrete-time systems with delays in state and delays in control, Bull. Pol. Acad. Sci. Tech., 53(3) (2005), 293-298.
- [21] T. Kaczorek: Positive stable realizations of continuous-time linear systems, Proc. Conf. Int. Inf. and Eng. Syst., Krynica-Zdrój, Poland, 17-21 September, 2012.
- [22] T. Kaczorek: Positive stable realizations for fractional descriptor continuous-time linear systems, Archives of Control Sciences, 22(3) (2012), 255-265.
- [23] T. Kaczorek: Positive stable realizations with system Metzler matrices, Archives of Control Sciences, 21(2) (2011), 167-188.
- [24] T. Kaczorek: Realization problem for fractional continuous-time systems, Archives of Control Sciences, 18(1) (2008), 43-58.
- [25] T. Kaczorek: Realization problem for positive 2D hybrid systems, COM-PEL, 27(3) (2008), 613-623.
- [26] T. Kaczorek: Realization problem for positive discrete-time systems with delays, System Science, 30(4), (2004), 117-130.
- [27] T. Kaczorek: Realization problem for positive multivariable discrete-time linear systems with delays in the stste vector and inputs, Int. J. Appl. Math Comput. Sci., 16(2) (2006), 169-174.
- [28] T. Kaczorek: Selected Problems of Fractional Systems Theory, Springer- Verlag, 2011.
- [29] T. Kaczorek and M. Busłowicz: Minimal realization for positive multivariable linear systems with delay, Int. J. Appl. Math. Comput. Sci., 14(2) (2004), 181-187.
- [30] T. Kaczorek and Ł. Sajewski: The Realization Problem for Positive and Fractional Systems, Springer, 2014.
- [31] K. B. Oldham and J. Spanier: The Fractional Calculus, Academic Press, New York, 1974.
- [32] P. Ostalczyk: Discrete Fractional Calculus: Selected Applications in Control and Image Processing, Series in Computer Vision, vol. 4, 2016.
- [33] P. Ostalczyk: Epitome of the fractional calculus: Theory and its Applications in Automatics, Wydawnictwo Politechniki Łódzkiej, Łódź, 2008.
- [34] I. Podlubny: Fractional Differential Equations, Academic Press, San Diego, 1999.
- [35] Ł. Sajewski: Descriptor fractional discrete-time linear system with two different fractional orders and its solution, Bull. Pol. Acad. Sci. Tech., 64(1) (2016), 15-20.
- [36] W. Xiang-Jun, W. Zheng-Mao, and L. Jun-Guo: Stability analysis of a class of nonlinear fractional-order systems, IEEE Trans. Circuits and Systems-II, Express Briefs, 55(11) (2008), 1178-1182.
Uwagi
EN
1. The studies have been carried out in the framework of work No. S/WE/1/2016 and financed from the funds for science by the Polish Ministry of Science and Higher Education.
PL
2. Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-60102eb1-73fa-4301-9c47-e2babec8d5be