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Positivity of fractional descriptor linear discrete-time systems

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EN
Abstrakty
EN
The positivity of fractional descriptor linear discrete-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 discrete-time systems are established. The discussion is illustrated with numerical examples.
Twórcy
  • Faculty of Electrical Engineering, Białystok University of Technology, Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
  • [1] Ali, R.M. and Napp, D. (2012). Characterization and stability of autonomous positive descriptor systems, IEEE Transactions on Automatic Control 57(10): 2668–2673.
  • [2] Berman, A. and Plemmons, R.J. (1994). Nonnegative Matrices in the Mathematical Sciences, SIAM, New York, NY.
  • [3] Borawski, K. (2018). Analysis of the positivity of descriptor continuous-time linear systems by the use of Drazin inverse matrix method, in R. Szewczyk et al. (Eds.), Automation 2018, Advances in Intelligent Systems and Computing, Vol. 743, Springer, Cham, pp. 172–182.
  • [4] Busłowicz, M. (2008). Stability of linear continuous-time fractional order systems with delays of the retarded type, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 319–324.
  • [5] Busłowicz, M. (2012). Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(2): 279–284.
  • [6] Busłowicz, M. and Kaczorek, T. (2009). Simple conditions for practical stability of positive fractional discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 19(2): 263–269, DOI: 10.2478/v10006-009-0022-6.
  • [7] Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY.
  • [8] Kaczorek, T. (1993). Theory of Control and Systems, Polish Scientific Publishers, Warsaw, (in Polish).
  • [9] Kaczorek, T. (1997). Positive singular discrete-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 45(4): 619–631.
  • [10] Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer, London.
  • [11] Kaczorek, T. (2008). 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.
  • [12] Kaczorek, T. (2010). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(3): 453–458.
  • [13] Kaczorek, T. (2011a). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuits and Systems 58(7): 1203–1210.
  • [14] Kaczorek, T. (2011b). Selected Problems of Fractional Systems Theory, Springer, Berlin.
  • [15] Kaczorek, T. (2012). Positive fractional continuous-time linear systems with singular pencils, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(1): 9–12.
  • [16] Kaczorek, T. (2013). Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils, International Journal of Applied Mathematics and Computer Science 23(1): 29–33, DOI: 10.2478/amcs-2013-0003.
  • [17] Kaczorek, T. (2014). Descriptor positive discrete-time and continuous-time nonlinear systems, Proceedings of SPIE 9290, DOI: 10.1117/12.2074558.
  • [18] Kaczorek, T. (2015a). Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems, Computational Problems of Electrical Engineering 5(1): 11–16.
  • [19] Kaczorek, T. (2015b). Positivity and stability of discrete-time nonlinear systems, IEEE 2nd International Conference on Cybernetics, Gdynia, Poland, pp. 156–159.
  • [20] Kaczorek, T. (2015c). Stability of fractional positive nonlinear systems, Archives of Control Sciences 25(4): 491–496, DOI: 10.1515/acsc-2015-0031.
  • [21] Kaczorek, T. (2016a). Analysis of positivity and stability of fractional discrete-time nonlinear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 64(3): 491–494.
  • [22] Kaczorek, T. (2016b). Drazin inverse matrix method for fractional descriptor discrete-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 64(2): 395–399.
  • [23] Kaczorek, T. (2018). Stability of interval positive continuous-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 66(1): 2018.
  • [24] Kaczorek, T. (2019). 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): 299–307.
  • [25] Klamka, J. (2002). Positive controllability of positive dynamical systems, Proceedings of the American Control Conference, ACC-2000, Anchorage, AK, USA, pp. 4395–4400.
  • [26] Mitkowski, W. (2000). Remarks on stability of positive linear systems, Control and Cybernetics 29(1): 295–304.
  • [27] Mitkowski, W. (2008). Dynamical properties of Metzler systems, Bulletin of the Polish Academy of Sciences, Technical Sciences 56(4): 309–312.
  • [28] Sajewski, Ł. (2016a). Descriptor fractional discrete-time linear system and its solution—Comparison of three different methods, in R. Szewczyk et al. (Eds.), Challenges in Automation, Robotics and Measurement Techniques, Advances in Intelligent Systems and Computing, Vol. 440, Springer, Berlin/Heidelberg, pp. 37–50.
  • [29] Sajewski, Ł. (2016). Descriptor fractional discrete-time linear system with two different fractional orders and its solution, Bulletin of the Polish Academy of Sciences, Technical Sciences 64(1): 15–20.
  • [30] Zhang, H., Xie, D., Zhang, H. and Wang, G. (2014a). Stability analysis for discrete-time switched systems with unstable subsystems by a mode-dependent average dwell time approach, ISA Transactions 53(10): 1081–1086.
  • [31] Zhang, J, Han, Z., Wu, H. and Hung, J. (2014b). Robust stabilization of discrete-time positive switched systems with uncertainties and average dwell time switching, Circuits Systems and Signal Processing 33(1): 71–95.
  • [32] Xiang-Jun, W., Zheng-Mao, W. and Jun-Guo, L. (2008). Stability analysis of a class of nonlinear fractional-order systems, IEEE Transactions Circuits and Systems II: Express Briefs 55(11): 1178–1182.
Uwagi
PL
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-0f9d49ca-d249-476f-ab1f-c8b3cbc239b7
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