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

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.1515/amcs-2016-0001

• Języki publikacji: EN

Abstrakty

EN

The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor time-varying 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.

Słowa kluczowe

EN

fractional system; descriptor system; time varying system; positive system; discrete-time system

PL

układ ułamkowy; układ deskrypcyjny; układ dodatni; układ dyskretno-czasowy

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2016
• Tom: Vol. 26, no. 1
• Strony: 5--13
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Białystok University of Technology, ul. Wiejska 45D, 15-351 Białystok, Poland

Bibliografia

• [1] 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.
• [2] 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.
• [3] 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.
• [4] Czornik, A. and Niezabitowski, M. (2013a). Lyapunov exponents for systems with unbounded coefficients, Dynamical Systems: An International Journal 28(2): 140–153.
• [5] Czornik, A. and Niezabitowski, M. (2013b). On the stability of discrete time-varying linear systems, Nonlinear Analysis: Hybrid Systems 9: 27–41.
• [6] Czornik, A. and Niezabitowski, M. (2013c). On the stability of Lyapunov exponents of discrete linear system, European Control Conference, Zurich, Switzerland, pp. 2210–2213.
• [7] 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.
• [8] 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.
• [9] Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY.
• [10] Kaczorek, T. (1997). Positive singular discrete time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 45(4): 619–631.
• [11] Kaczorek, T. (1998a). Positive descriptor discrete-time linear systems, Problems of Nonlinear Analysis in Engineering Systems 1(7): 38–54.
• [12] Kaczorek, T. (1998b). Vectors and Matrices in Automation and Electrotechnics, WNT, Warsaw, (in Polish).
• [13] Kaczorek, T. (2001). Positive 1D and 2D Systems, Springer Verlag, London.
• [14] Kaczorek, T. (2011). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuits and Systems 58(6): 1203–1210.
• [15] Kaczorek, T. (2012). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
• [16] 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.
• [17] Kaczorek, T. (2015b). Positive descriptor time-varying discrete-time linear systems and their asymptotic stability, TransNav 9(1): 83–89.
• [18] 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.
• [19] 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, Mi˛edzyzdroje, Poland, pp. 880–884.
• [20] 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.
• [21] 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.
• [22] 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.
• [23] 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.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.