Absolute stability of a class of fractional positive nonlinear systems

• Autorzy: Kaczorek Tadeusz

Identyfikatory

DOI

10.2478/amcs-2019-0007

• Języki publikacji: EN

Abstrakty

EN

The positivity and absolute stability of a class of fractional nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of fractional positive nonlinear systems are also given.

Słowa kluczowe

EN

absolute stability; fractional system; positive system; nonlinear system

PL

stabilność absolutna; układ ułamkowy; układ dodatni; układ nieliniowy

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2019
• Tom: Vol. 29, no. 1
• Strony: 93--98
• Opis fizyczny: Bibliogr. 31 poz., rys.

Twórcy

autor

Kaczorek Tadeusz

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

Bibliografia

• [1] Ait Rami M. and Tadeo F. (2007). Controller synthesis for positive linear systems with bounded controls, IEEE Transactions on Circuits and Systems 54(2): 151–155.
• [2] Bartosiewicz, Z. (2017). On controllability of positive nonlinear continuous-time systems, Proceedings of the Asian Control Conference (ASCC), Gold Coast, Australia, pp. 298–302.
• [3] Berman, A. and Plemmons, R.J. (1994). Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, PA.
• [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. (2002). Positive 1D and 2D Systems, Springer, London.
• [9] Kaczorek, T. (2010). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(3): 453–458.
• [10] Kaczorek, T. (2011a). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuits and Systems 5897: 1203–1210.
• [11] Kaczorek, T. (2011b). Selected Problems of Fractional Systems Theory, Springer, Berlin.
• [12] Kaczorek, T. (2014). Descriptor positive discrete-time and continuous-time nonlinear systems, Proceedings of SPIE 9290: 92902Q.
• [13] Kaczorek, T. (2015a). Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems, Computational Problems of Electrical Engineering 5(1): 127–130.
• [14] Kaczorek, T. (2015b). Positivity and stability of discrete-time nonlinear systems, IEEE 2nd International Conference on Cybernetics, Gdynia, Poland, pp. 156–159.
• [15] Kaczorek, T. (2015c). Stability of fractional positive nonlinear systems, Archives of Control Sciences 25(4): 491–496.
• [16] Kaczorek, T. (2016). Analysis of positivity and stability of fractional discrete-time nonlinear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 64(3): 491–494.
• [17] Kaczorek, T. (2018). Decentralized stabilization of fractional positive descriptor continuous-time linear systems, International Journal of Applied Mathematics and Computer Science 28(1): 135–140, DOI: 10.2478/amcs-2018-0010.
• [18] Mitkowski, W. (2008). Dynamical properties of Metzler matrices, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 309–312.
• [19] Oldham, K.B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY.
• [20] Ortigueira M.D. (2011). Fractional Calculus for Scientists and Engineers, Springer, Berlin/Heidelberg.
• [21] Ostalczyk P. (2008). Epitome of the Fractional Calculus: Theory and Its Applications in Automatics, Lodz University of Technology Press, Łódź, (in Polish).
• [22] Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA.
• [23] Polyak B.T. and Shcherbakov P.S. (2002a). Superstable linear control systems. I: Analysis, Automation and Remote Control 63(8): 1239–1254.
• [24] Polyak B.T. and Shcherbakov P.S. (2002b). Superstable Linear Control Systems, II: Design, Automation and Remote Control 63(11): 1745–1763.
• [25] Radwan, A.G., Soliman, A.M., Elwakil, A.S. and Sedeek, A. (2009). On the stability of linear systems with fractional-order elements, Chaos, Solitons and Fractals 40(5): 2317–2328.
• [26] Sajewski, Ł. (2017a). Decentralized stabilization of descriptor fractional positive continuous-time linear systems with delays, 22nd International Conference on Methods and Models in Automation and Robotics (MMAR), Międzyzdroje, Poland, pp. 482–487.
• [27] Sajewski Ł. (2017b). Stabilization of positive descriptor fractional discrete-time linear system with two different fractional orders by decentralized controller, Bulletin of the Polish Academy of Sciences: Technical Sciences 65(5): 709–714.
• [28] Solteiro Pires, E.J., Tenreiro Machado, J.A., Moura Oliveira, P.B. (2006), Functional dynamics in genetic algorithms, Workshop on Fractional Differentiation and Its Application, Porto, Portugal, 414–419.
• [29] Vinagre, B.M., Monje, C.A. and Calderon, A.J. (2002). Fractional order systems and fractional order control actions, Proceedings of the Conference on Decision and Control CDC’02, Las Vegas, NV, USA, pp. 2550–2554.
• [30] Zhang, J., Han, Z. Wu, H. and Hung, J. (2014). Robust stabilization of discrete-time positive switched systems with uncertainties and average dwell time switching, Circuits Systems and Signal Processing 33: 71–95.
• [31] Xiang-Jun, W., Zheng-Mao, W. and Jun-Guo, L. (2008). Stability analysis of a class of nonlinear fractional-order systems, IEEE Transactions on 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).