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Invariant properties of positive linear electrical circuits

Treść / Zawartość
Warianty tytułu
Konferencja
Computer Applications in Electrical Engineering (15-16.04.2019 ; Poznań, Polska)
Języki publikacji
EN
Abstrakty
EN
The invariant properties of the stability, reachability, and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.
Słowa kluczowe
Rocznik
Tom
Strony
109--123
Opis fizyczny
Bibliogr. 33 poz., rys.
Twórcy
  • Bialystok University of Technology
Bibliografia
  • [1] Benvenuti L., Farina L., A tutorial on the positive realization problem. IEEE Trans. on Automatic Control. 49(5), 2004, pp. 651–664.
  • [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. 56(4), 2008, pp. 319–324.
  • [4] Busłowicz M., Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders. Bull. Pol. Acad. Sci. Tech. 60(2), 2012, pp. 279–284.
  • [5] Busłowicz M., Kaczorek T., Simple conditions for practical stability of positive fractional discrete-time linear systems. Int. J. Appl. Math. Comput. Sci. 19(2), 2009, pp. 263–269.
  • [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. 22(4), 2012, pp. 897–905.
  • [8] Kaczorek T., A realization problem for positive continuous-time linear systems with reduced numbers of delays. Int. J. Appl. Math. Comput. Sci. 16(3), 2006, pp. 325–331.
  • [9] Kaczorek T., Computation of positive stable realizations for linear continuoustime systems. Bull. Pol. Acad. Techn. Sci. 59(3), 2011, pp. 273–281.
  • [10] Kaczorek T., Computation of realizations of discrete-time cone systems. Bull. Pol. Acad. Sci. Techn. 54(3), 2006, pp. 347–350.
  • [11] Kaczorek T., Existence and determination of the set of Metzler matrices for given stable polynomials. Int. J. Appl. Math. Comput. Sci. 22(2), 2012, pp. 389–399.
  • [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. 53(3), 2005, pp. 293–298.
  • [15] Kaczorek T., Positive stable realizations of continuous-time linear systems. Proc. Conf. Int. Inf. and Eng. Syst., Krynica-Zdrój, Poland, 17–21 September, 2012.
  • [16] Kaczorek T., Positive stable realizations for fractional descriptor continuous-time linear systems. Archives of Control Sciences. 22(3), 2012, pp. 255–265.
  • [17] Kaczorek T., Positive stable realizations with system Metzler matrices. Archives of Control Sciences. 21(2), 2011, pp. 167–188.
  • [18] Kaczorek T., Realization problem for fractional continuous-time systems. Archives of Control Sciences. 18(1), 2008, pp. 43–58.
  • [19] Kaczorek T., Realization problem for positive 2D hybrid systems. COMPEL. 27(3), 2008, pp. 613–623.
  • [20] Kaczorek T., Realization problem for positive discrete-time systems with delays. System Science. 30(4), 2004, pp. 117–130.
  • [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. 16(2), 2006, pp. 169–174.
  • [22] Kaczorek T., Relationship between the observability of standard and fractional linear systems,Advances in Intelligent Systems and Computing, Springer vol. 577. Editors: Wojciech Mitkowski, Janusz Kacprzyk, Krzysztof Oprzędkiewicz, Paweł Skruch, in Trends in Advanced Intelligent Control, Optimization and Automation, Proceedings of KKA The 19th Polish Control Conference, Kraków, Poland, June 18–21, 2017, pp. 455–459
  • [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] Klamka J., Relationships between controllability of standard and fractional linear systems, Advances in Intelligent Systems and Computing, Springer vol. 577. Editors: Wojciech Mitkowski, Janusz Kacprzyk, Krzysztof Oprzędkiewicz, Paweł Skruch, in Trends in Advanced Intelligent Control, Optimization and Automation, Proceedings of KKA The 19th Polish Control Conference, Kraków, Poland, June 18–21, 2017, pp. 455–459.
  • [26] Kaczorek T., Sajewski L., Invariant properties of positive linear systems with integer and fractional orders.Proc.Conf.Automation 2019.
  • [27] Kaczorek T., Sajewski L., Transfer matrices with positive coefficients of standard and fractional positive linear systems,Proc.MMAR Conf., Miedzyzdroje 2018 http:/ieeeexplore.ieee.org.
  • [28] Kaczorek T., Sajewski L., The Realization Problem for Positive and Fractional Systems, Springer, 2014.
  • [29] Oldham K.B., Spanier J., The Fractional Calculus. Academic Press, New York, 1974.
  • [30] Ostalczyk P., Discrete Fractional Calculus: Selected Applications in Control and Image Processing. Series in Computer Vision, vol. 4, 2016.
  • [31] Ostalczyk P., Epitome of the fractional calculus: Theory and its Applications in Automatics, Wydawnictwo Politechniki Łódzkiej, Łódź, 2008.
  • [32] Podlubny I., Fractional Differential Equations. Academic Press, San Diego, 1999.
  • [33] Sajewski L., Positive stable realization of fractional discrete-time linear systems, Asian Journal of Control, 16(3), 2014, pp. 922–927.
Uwagi
This work was supported by National Science Centre in Poland under work No. 2017/27/B/ST7/02443.
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
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