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Positivity of fractional descriptor linear continuous-time systems

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Języki publikacji
EN
Abstrakty
EN
The positivity of fractional descriptor linear continuous-time systems is investigated. The solution to the state equation of the systems is derived. Necessary and sufficient conditions for the positivity of fractional descriptor linear continuous-time systems are established. The considerations are illustrated by numerical examples.
Twórcy
autor
  • Białystok University of Technology, 45D Wiejska St., 15-351 Białystok, Poland
Bibliografia
  • [1] A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, 1994.
  • [2] L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
  • [3] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
  • [4] T. Kaczorek, “Analysis of positivity and stability of fractional discrete-time nonlinear systems”, Bull. Pol. Ac.: Tech. 64(3), 2016, 491‒494.
  • [5] T. Kaczorek, “Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems”, Computational Problems of Electrical Engineering 5(1), 2015.
  • [6] T. Kaczorek, “Descriptor positive discrete-time and continuous-time nonlinear systems”, Proc. of SPIE 9290, 2014, DOI. 10.1117/12.2074558.
  • [7] T. Kaczorek, “Positivity and stability of discrete-time nonlinear systems”, IEEE 2nd International Conference on Cybernetics, 2015, 156‒159.
  • [8] T. Kaczorek, “Stability of fractional positive nonlinear systems”, Archives of Control Sciences 25(4), 2015, 491‒496, DOI: 10.1515/acsc-2015‒0031.
  • [9] M. Busłowicz, “Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders”, Bull. Pol. Ac.: Tech. 60(2), 2012, 279‒284.
  • [10] T. Kaczorek, “Positive linear systems with different fractional orders”, Bull. Pol. Ac.: Tech. 58(3), 2010, 453‒458.
  • [11] T. Kaczorek, “Positive linear systems consisting of n subsystems with different fractional orders”, IEEE Trans. on Circuits and Systems 58(7), 2011, 1203‒1210.
  • [12] T. Kaczorek, “Drazin inverse matrix method for fractional descriptor discrete-time linear systems”, Bull. Pol. Ac.: Tech., 64(2), 2016, 395‒399.
  • [13] T. Kaczorek, “Positivity and stability of standard and fractional descriptor continuous-time linear and nonlinear systems”, International Journal of Nonlinear Sciences and Numerical Simulation 19(3‒4), 2018, 299‒307.
  • [14] T. Kaczorek, “Positive fractional continuous-time linear systems with singular pencils”, Bull. Pol. Ac.: Tech. 60(1), 2012, 9‒12.
  • [15] T. Kaczorek, “Positive singular discrete-time linear systems”, Bull. Pol. Ac.: Tech. 45(4), 1997, 619‒631.
  • [16] T. Kaczorek, Theory of Control and Systems, PWN, Warszawa, 1993 (in Polish).
  • [17] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer, Berlin, 2011.
  • [18] 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.
  • [19] T. Kaczorek, “Fractional positive continuous-time linear systems and their reachability”, Int. J. Appl. Math. Comput. Sci. 18(2), 2008, 223‒228.
  • [21] T. Kaczorek, “Application of Drazin inverse to analysis of descriptor fractional discrete-time linear systems with regular pencils”, Int. J. Appl. Math. Comput. Sci. 23(1), 2013, 29‒34.
  • [22] H. Zhang, D. Xie, H. Zhang, and G. Wang, “Stability analysis for discrete-time switched systems with unstable subsystems by a mode-dependent average dwell time approach”, ISA Transactions 53, 2014, 1081‒1086.
  • [23] Ł. Sajewski, “Descriptor fractional discrete-time linear system with two different fractional orders and its solution”, Bull. Pol. Ac.: Tech. 64(1), 2016, 15‒20.
  • [24] M. Busłowicz, Stability of linear continuous-time fractional order systems with delays of the retarded type, Bull. Pol. Ac.: Tech. 56(4, 2008, 319‒324.
  • [25] M. Busłowicz and T. Kaczorek, “Simple conditions for practical stability of positive fractional discrete-time linear systems”, Int. J. Appl. Math. Comput. Sci. 19(2), 2009, 263‒169.
  • [26] T. Kaczorek, “Stability of interval positive continuous-time linear systems”, Bull. Pol. Ac.: Tech. 66(1), 2018.
  • [27] M. Ali Rami and D. Napp, “Characterization and stability of autonomous positive descriptor systems”, IEEE Trans. Autom. Contr. 57(10), 2012, 2668‒2673.
  • [28] J. Zhang, Z. Han, H. Wu, and J. Hung, “Robust stabilization of discrete-time positive switched systems with uncertainties and average dwell time switching”, Circuits Syst. Signal Process. 33, 2014, 71‒95.
Uwagi
EN
This work was supported by National Science Centre in Poland under work No. 2017/27/B/ST7/02443.
PL
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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