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2016 | 26 | 1 | 5-13
Tytuł artykułu

Positivity and stability of fractional descriptor time-varying discrete-time linear systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor timevarying discrete-time linear systems. A method for computing solutions of fractional systems is proposed. Necessary and sufficient conditions for the positivity of these systems are established.
Rocznik
Tom
26
Numer
1
Strony
5-13
Opis fizyczny
Daty
wydano
2016
otrzymano
2014-11-08
poprawiono
2015-03-12
Twórcy
  • Faculty of Electrical Engineering, Białystok University of Technology, ul. Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
  • Czornik, A. (2014). The relations between the senior upper general exponent and the upper Bohl exponents, 19th International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 897-902.
  • Czornik, A., Newrat, A., Niezabitowski, M., Szyda, A. (2012). On the Lyapunov and Bohl exponent of time-varying discrete linear systems, 20th Mediterranean Conference on Control and Automation (MED), Barcelona, Spain, pp. 194-197.
  • Czornik, A., Newrat, A. and Niezabitowski, M. (2013). On the Lyapunov exponents of a class of the second order discrete time linear systems with bounded perturbations, Dynamical Systems: An International Journal 28(4): 473-483.
  • Czornik, A. and Niezabitowski, M. (2013a). Lyapunov exponents for systems with unbounded coefficients, Dynamical Systems: An International Journal 28(2): 140-153.
  • Czornik, A. and Niezabitowski, M. (2013b). On the stability of discrete time-varying linear systems, Nonlinear Analysis: Hybrid Systems 9: 27-41.
  • Czornik, A. and Niezabitowski, M. (2013c). On the stability of Lyapunov exponents of discrete linear system, European Control Conference, Zurich, Switzerland, pp. 2210-2213.
  • Czornik, A., Klamka, J. and Niezabitowski, M. (2014a). About the number of the lower Bohl exponents of diagonal discrete linear time-varying systems, 11th IEEE International Conference on Control & Automation, Taichung, Taiwan, pp. 461-466.
  • Czornik, A., Klamka, J. and Niezabitowski, M. (2014b). On the set of Perron exponents of discrete linear systems, World Congress of the 19th International Federation of Automatic Control, Kapsztad, South Africa, pp. 11740-11742.
  • Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY.
  • Kaczorek, T. (1997). Positive singular discrete time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 45(4): 619-631.
  • Kaczorek, T. (1998a). Positive descriptor discrete-time linear systems, Problems of Nonlinear Analysis in Engineering Systems 1(7): 38-54.
  • Kaczorek, T. (1998b). Vectors and Matrices in Automation and Electrotechnics, WNT, Warsaw, (in Polish).
  • Kaczorek, T. (2001). Positive 1D and 2D Systems, Springer Verlag, London.
  • Kaczorek, T. (2011). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuits and Systems 58(6): 1203-1210.
  • Kaczorek, T. (2012). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
  • Kaczorek, T. (2015a). Fractional descriptor standard and positive discrete-time nonlinear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 63(3): 651-655.
  • Kaczorek, T. (2015b). Positive descriptor time-varying discrete-time linear systems and their asymptotic stability, TransNav 9(1): 83-89.
  • Kaczorek, T. (2015c). Positivity and stability of time-varying discrete-time linear systems, in N.T. Nguyen et al. (Eds.), Intelligent Information and Database Systems, Lecture Notes in Computer Science, Vol. 9011, Springer, Berlin/Heidelberg, pp. 295-303.
  • Niezabitowski, M. (2014). About the properties of the upper Bohl exponents of diagonal discrete linear time-varying systems, 19th International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 880-884.
  • Rami, M.A., Bokharaie, V.S., Mason, O. and Wirth, F.R. (2012). Extremal norms for positive linear inclusions, 20th International Symposium on Mathematical Theory of Networks and Systems, Melbourne, Australia, pp. 1-8.
  • 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(4): 1081-1086.
  • 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.
  • Zhong, Q., Cheng, J. and Zhong, S. (2013). Finite-time H∞ control of a switched discrete-time system with average dwell time, Advances in Difference Equations 2013, Article ID: 191.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv26i1p5bwm
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