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Invariant properties of positive linear electrical circuits

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The invariant properties of the stability, reachability, observability and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability, observability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.
Rocznik
Strony
875--890
Opis fizyczny
Bibliogr. 32 poz., rys., wz.
Twórcy
  • Faculty of Electrical Engineering University of Technology Wiejska 45D, 15-351 Bialystok
Bibliografia
  • [1] Benvenuti L., Farina L., A tutorial on the positive realization problem, IEEE Trans. on Automatic Control., vol. 49, no. 5, pp. 651–664 (2004).
  • [2] Berman A., Plemmons R.J., Nonnegative Matrices in the Mathematical Sciences, SIAM (1994).
  • [3] Busłowicz M., Stability of linear continuous-time fractional order systems with delays of the retarded type, Bull. Pol. Acad. Sci. Tech., vol. 56, no. 4, pp. 319–324 (2008).
  • [4] Busłowicz M., Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders, Bull. Pol. Acad. Sci. Tech., vol. 60, no. 2, pp. 279–284 (2012).
  • [5] Busłowicz M., Kaczorek T., Simple conditions for practical stability of positive fractional discrete-time linear systems, Int. J. Appl. Math. Comput. Sci., vol. 19, no. 2, pp. 263–269 (2009).
  • [6] Farina L., Rinaldi S., Positive Linear Systems; Theory and Applications, J. Wiley, New York (2000).
  • [7] Kaczorek T., A modified state variable diagram method for determination of positive realizations of linear continuous-time systems with delays, Int. J. Appl. Math. Comput. Sci., vol. 22, no. 4, pp. 897–905 (2012).
  • [8] Kaczorek T., A realization problem for positive continuous-time linear systems with reduced numbers of delays, Int. J. Appl. Math. Comput. Sci., vol. 16, no. 3, pp. 325–331 (2006).
  • [9] Kaczorek T., Computation of positive stable realizations for linear continuous-time systems, Bull. Pol. Acad. Techn. Sci., vol. 59, no. 3, pp. 273–281 (2011).
  • [10] Kaczorek T., Computation of realizations of discrete-time cone systems, Bull. Pol. Acad. Sci. Techn., vol. 54, no. 3, pp. 347–350 (2006).
  • [11] Kaczorek T., Existence and determination of the set of Metzler matrices for given stable polynomials, Int. J. Appl. Math. Comput. Sci., vol. 22, no. 2, pp. 389–399 (2012).
  • [12] Kaczorek T., Linear Control Systems: Analysis of Multivariable Systems, J. Wiley & Sons, New York (1992).
  • [13] Kaczorek T., Positive 1D and 2D Systems, Springer-Verlag, London (2002).
  • [14] Kaczorek T., Positive minimal realizations for singular discrete-time systems with delays in state and delays in control, Bull. Pol. Acad. Sci. Tech., vol. 53, no. 3, pp. 293–298 (2005).
  • [15] Kaczorek T., Positive stable realizations of continuous-time linear systems, Proc. Conf. Int. Inf. and Eng. Syst., Krynica-Zdrój, Poland, pp. 17–21 September (2012).
  • [16] Kaczorek T., Positive stable realizations for fractional descriptor continuous-time linear systems, Archives of Control Sciences, vol. 22, vol. 3, pp. 255–265 (2012).
  • [17] Kaczorek T., Positive stable realizations with system Metzler matrices, Archives of Control Sciences, vol. 21, no. 2, pp. 167–188 (2011).
  • [18] Kaczorek T., Realization problem for fractional continuous-time systems, Archives of Control Sciences, vol. 18, no. 1, pp. 43–58 (2008).
  • [19] Kaczorek T., Realization problem for positive 2D hybrid systems, COMPEL, vol. 27, no. 3, pp. 613–623 (2008).
  • [20] Kaczorek T., Realization problem for positive discrete-time systems with delays, System Science, vol. 30, no. 4, pp. 117–130 (2004).
  • [21] Kaczorek T., Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs, Int. J. Appl. Math. Comput. Sci., vol. 16, no. 2, pp. 169–174 (2006).
  • [22] Kaczorek T., Relationship between the observability of standard and fractional linear systems, Archives of Control Sciences, vol. 27, no. 3, pp. 441–451 (2017).
  • [23] Kaczorek T., Selected Problems of Fractional Systems Theory, Springer-Verlag (2011).
  • [24] Klamka J., Controllability of Dynamical Systems, Kluwer Academic Press, Dordrecht (1991).
  • [25] Kaczorek T., Sajewski Ł., Transfer matrices with positive coefficients of positive descriptor continuoustime linear systems, in: Szewczyk R., Zieliński C., Kaliczyńska M. (eds) Automation 2019, Advancesin Intelligent Systems and Computing, Springer, Cham, vol. 920, pp. 86–94 (2020).
  • [26] Kaczorek T., Sajewski Ł., Transfer matrices with positive coefficients for standard and fractional positive linear systems, 23nd International Conference on Methods and Models in Automation and Robotics (MMAR), Miedzyzdroje, Poland (2018).
  • [27] Kaczorek T., Sajewski Ł., The Realization Problem for Positive and Fractional Systems, Springer (2014).
  • [28] Oldham K.B., Spanier J., The Fractional Calculus, Academic Press, New York (1974).
  • [29] Ostalczyk P., Discrete Fractional Calculus: Selected Applications in Control and Image Processing, Series in Computer Vision, vol. 4 (2016).
  • [30] Ostalczyk P., Epitome of the fractional calculus: Theory and its Applications in Automatics, Wydawnictwo Politechniki Łódzkiej, Łódź (2008).
  • [31] Podlubny I., Fractional Differential Equations, Academic Press, San Diego (1999).
  • [32] Sajewski Ł., Positive stable realization of fractional discrete-time linear systems, Asian Journal of Control, vol. 16, no. 3, pp. 922–927 (2014)
Uwagi
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-0ad7748d-13a6-4653-ae48-357852178000
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