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2016 | 26 | 3 | 533-541
Tytuł artykułu

Fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative

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 continuous-time linear systems described by the Caputo-Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated with a numerical example.
Rocznik
Tom
26
Numer
3
Strony
533-541
Opis fizyczny
Daty
wydano
2016
otrzymano
2015-11-26
poprawiono
2016-02-29
zaakceptowano
2016-05-25
Twórcy
  • Faculty of Electrical Engineering, Białystok Technical University, Wiejska 45D, 15-351 Białystok, Poland
  • Faculty of Electrical Engineering, Białystok Technical University, Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
  • Bru, R., Coll, C., Romero-Vivo, S. and Sanchez, E. (2003). Some problems about structural properties of positive descriptor systems, in L. Benvenuti et al. (Eds.), Positive Systems, Lecture Notes in Control and Information Sciences, Vol. 294, Springer, Berlin, pp. 233-240.
  • Bru, R., Coll, C. and Sanchez, E. (2000). About positively discrete-time singular systems, in M.E. Mastorakis (Ed.), System and Control: Theory and Applications, World Scientific and Engineering Society, Athens, pp. 44-48.
  • Campbell, S.L., Meyer, C. and Rose, N. (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.
  • Caputo, M. and Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel, Progress in Fractional Differentiation and Applications 1(2): 1-13.
  • Dai, L. (1989). Singular Control Systems, Lecture Notes in Control and Information Sciences, Vol. 118, Springer-Verlag, Berlin.
  • Dodig, M. and Stosic, M. (2009). Singular systems state feedbacks problems, Linear Algebra and Its Applications 431(8): 1267-1292.
  • Duan, G.R. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY.
  • 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.
  • Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY.
  • Gantmacher, F.R. (1959). The Theory of Matrices, Chelsea Publishing Company, London.
  • 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. (2011a). New stability tests of positive standard and fractional linear systems, Circuits and Systems 2(4): 261-268.
  • Kaczorek, T. (2011b). 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. (2014a). Descriptor positive discrete-time and continuous-time nonlinear systems, 34 IEEE-SPIE Joint Symposium, Wilga, Poland, DOI:10.1117/12.2074558.
  • Kaczorek, T. (2014b). Positivity and linearization of a class of nonlinear discrete-time systems by state feedbacks, Logistyka (6): 5078-5083.
  • Kaczorek, T. (2015a). Analysis of positive and stable fractional continuous-time linear systems by the use of Caputo-Fabrizio derivative, 12th International Conference on Mechatronic Systems and Materials (MSM'2016), Białystok, Poland.
  • Kaczorek, T. (2015b). Positivity and stability of discrete-time nonlinear systems, IEEE 2nd International Conference on Cybernetics (CYBCONF), Gdynia, Poland.
  • Klamka, J. (2013). Controllability of dynamical systems: A survey, Bulletin of the Polish Academy of Sciences: Technical Sciences 61(2): 221-229.
  • Kucera, V. and Zagalak, P. (1988). Fundamental theorem of state feedback for singular systems, Automatica 24(5): 653-658.
  • Losada, J. and Nieto, J. (2015). Properties of a new fractional derivative without singular kernel, Progress in Fractional Differentiation and Applications 1(2): 87-92.
  • Ostalczyk, P. (2016). Discrete Fractional Calculus, World Scientific Publishing Company, River Edge, NJ.
  • Van Dooren, P. (1979). The computation of Kronecker's canonical form of a singular pencil, Linear Algebra and Its Applications 27: 103-140.
  • Virnik, E. (2008). Stability analysis of positive descriptor systems, Linear Algebra and Its Applications 429(10): 2640-2659.
  • 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.
Typ dokumentu
Bibliografia
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