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Abstrakty
Descriptor and standard linear continuous-time systems with different fractional orders are investigated. Descriptor systems are analyzed making use of the Drazin matrix inverse. Necessary and sufficient conditions for the pointwise completeness and pointwise degeneracy of descriptor continuous-time linear systems with different fractional orders are derived. It is shown that (i) the descriptor linear continuous-time system with different fractional orders is pointwise complete if and only if the initial and final states belong to the same subspace, (ii) the descriptor linear continuous-time system with different fractional orders is not pointwise degenerated in any nonzero direction for all nonzero initial conditions. Results are reported for the case of two different fractional orders and can be extended to any number of orders.
Rocznik
Tom
Strony
641--647
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
- Faculty of Electrical Engineering, Białystok University of Technology, Wiejska 45D, 15-351 Białystok, Poland
autor
- Faculty of Electrical Engineering, Białystok University of Technology, Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
- [1] Bingi, K., Ibrahim, R., Karsiti, M.N., Hassam, S.M. and Harindran, V.R. (2019). Frequency response based curve fitting approximation of fractional-order PID controllers, International Journal of Applied Mathematics and Computer Science 29(2): 311–326, DOI: 10.2478/amcs-2019-0023.
- [2] 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, Springer, Cham, pp. 172–182.
- [3] 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.
- [4] Campbell, S.L., Meyer, C.D. and Rose, N.J. (1976). Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients, SIAM Journal on Applied Mathematics 31(3): 411–425.
- [5] Dai, L. (1989). Singular Control Systems, Springer, Berlin.
- [6] Djennoune, S., Bettayeb, M. and Al-Saggaf, U.M. (2019). Synchronization of fractional-order discrete-time chaotic systems by an exact delayed state reconstructor: Application to secure communication, International Journal of Applied and Mathematics and Computer Science 29(1): 179–194, DOI: 10.2478/amcs-2019-0014.
- [7] Dzieliński, A., Sierociuk, D. and Sarwas, G. (2009). Ultracapacitor parameters identification based on fractional order model, Proceedings of the European Control Conference, Budapest, Hungary, pp. 196–200.
- [8] Fahmy, M.M. and O’Reilly, J. (1989). Matrix pencil of closed-loop descriptor systems: Infinite-eigenvalues assignment, International Journal of Control 49(4): 1421–1431.
- [9] Ferreira, N.M.F. and Machado, J.A.T. (2003). Fractional-order hybrid control of robotic manipulators, 11th International Conference on Advanced Robotics, ICAR, Coimbra, Portugal, pp. 393–398.
- [10] Guang-Ren, D. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY.
- [11] Kaczorek, T. (2009). Fractional positive linear systems, Kybernetes: The International Journal of Systems and Cybernetics 38(7/8): 1059–1078.
- [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. (2011). Selected Problems in Fractional Systems Theory, Springer, Berlin.
- [14] Kaczorek, T. (2014). Drazin inverse matrix method for fractional descriptor continuous-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 62(3): 409–412.
- [15] Kaczorek, T. (2015). Pointwise completeness and pointwise degeneracy of fractional descriptor continuous-time linear systems with regular pencils, Bulletin of the Polish Academy of Sciences: Technical Sciences 63(1): 169–172.
- [16] Kaczorek, T. (2019). Absolute stability of a class of fractional positive nonlinear systems, International Journal of Applied Mathematics and Computer Science 29(1): 93–98, DOI: 10.2478/amcs-2019-0007.
- [17] Kaczorek, T. (2020). Global stability of positive standard and fractional nonlinear feedback systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 68(2): 285–288.
- [18] Kaczorek, T. and Busłowicz, M. (2009). Pointwise completeness and pointwise degeneracy of linear continuous-time fractional order systems, Journal of Automation, Mobile Robotics and Intelligent Systems 3(1): 8–11.
- [19] Kaczorek, T. and Rogowski, K. (2015). Fractional Linear Systems and Electrical Circuits, Springer, Cham.
- [20] Korobov, A.A. (2017). On pointwise degenerate linear delay-differential systems with nonnilpotent passive matrices, Journal of Applied and Industrial Mathematics 11(3): 369–380.
- [21] Kucera, V. and Zagalak, P. (1988). Fundamental theorem of state feedback for singular systems, Automatica 24(5): 653–658.
- [22] Metel’skii, A.V. and Karpuk, V.V. (2009). On properties of pointwise degenerate linear autonomous control systems I, Automation and Remote Control 70(10): 1613–1625.
- [23] Miller, K.S. and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY.
- [24] Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA.
- [25] Sajewski, Ł. (2015). Minimum energy control of fractional positive continuous-time linear systems with two different fractional orders and bounded inputs, in K. Latawiec et al. (Eds), Advances in Modelling and Control of Non-integer-Order Systems, Springer, Cham, pp. 171–181.
- [26] Sajewski, Ł. (2016). Reachability, observability and minimum energy control of fractional positive continuous-time linear systems with two different fractional orders, Multidimensional Systems and Signal Processing 27(1): 27–41.
- [27] Trzasko, W. (2014). Pointwise completeness and pointwise degeneracy of linear continuous-time systems with different fractional orders, in R. Szewczyk et al. (Eds), Recent Advances in Automation, Robotics and Measuring Techniques, Springer, Cham, pp. 307–316.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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