Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The stability problems of fractional discrete-time linear scalar systems described by the new model are considered. Using the classical D-partition method, the necessary and sufficient conditions for practical stability and asymptotic stability are given. The considerations are il-lustrated by numerical examples.
Czasopismo
Rocznik
Tom
Strony
441--452
Opis fizyczny
Bibliogr. 24 poz., rys., wzory
Twórcy
autor
- Bialystok University of Technology, Faculty of Electrical Engineering, ul. Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
- [1] S. Das: Functional Fractional Calculus for System Identification and Controls. Springer, Berlin 2008.
- [2] M. Busłowicz: Stability of state-space models of linear continuous-time fractional order systems. Acta Mechanica et Automatica, 5 (2011), 15-22.
- [3] M. Busłowicz: 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 (2012), 279-284.
- [4] M. Busłowicz: Simple analytic conditions for stability of fractional discretetime linear systems with diagonal state matrix. Bulletin of the Polish Academy of Sciences, Technical Sciences, 60 (2012), 809-814.
- [5] M. Busłowicz: Stability of fractional discrete-time linear scalar systems with one delay. Pomiary Automatyka Robotyka, 2 (2013).
- [6] M. Busłowicz: Stability conditions for linear continuous-time fractional-order state-delayed systems. Bulletin of the Polish Academy of Sciences, Technical Sciences, 64 (2016), 3-7.
- [7] M. Busłowicz and T. Kaczorek: Simple conditions for practical stability of linear positive fractional discrete-time linear systems. Int. J. of Applied Mathematics and Computer Science, 19 (2009), 263-269.
- [8] M. Busłowicz and A. Ruszewski: Necessary and sufficient conditions for stability of fractional discrete-time linear state-space systems. Bulletin of the Polish Academy of Sciences, Technical Sciences, 61 (2013), 779-786.
- [9] A. Dzieliński and D. Sierociuk: Stability of discrete fractional state-space systems. J. of Vibration and Control, 14 (2008), 1543-1556.
- [10] E. N. Gryazina, B. T. Polyak and A. A. Tremba: D-decomposition technique state-of-the-art. Automation and Remote Control, 69(12), (2008), 1991-2026.
- [11] T. Kaczorek: Practical stability of positive fractional discrete-time systems. Bulletin of the Polish Academy of Sciences, Technical Sciences, 56 (2008), 313-317.
- [12] T. Kaczorek: Selected Problems of Fractional Systems Theory. Springer, Berlin (2011).
- [13] T. Kaczorek and P. Ostalczyk: Responses comparison of the two discretetime linear fractional state-space models. Fractional Calculus and Applied Analysis, 19 (2016), 789-805.
- [14] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006).
- [15] C. Monje, Y. Chen, B. Vinagre, D. Xue and V. Feliu: Fractional-order Systems and Controls. Springer-Verlag, London (2010).
- [16] K. Oprzędkiewicz and E. Gawin: A non integer order, state space model for one dimensional heat transfer process. Archives of Control Sciences, 26 (2016), 261-275.
- [17] P. Ostalczyk: Epitome of the fractional calculus. Theory and its applications in automatics. Publishing Department of Technical University of Łód´z, Łód´z, 2008, (in Polish).
- [18] P. Ostalczyk: Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains. Int. J. Applied Mathematics and Computer Science, 22 (2012), 533-538.
- [19] I. Petras: Stability of fractional-order systems with rational orders: a survey. Fractional Calculus & Applied Analysis. An Int. J. for Theory and Applications, 12 (2009), 269-298.
- [20] I. Podlubny: Fractional Differential Equations. Academic Press, San Diego (1999).
- [21] A. Ruszewski: Stability conditions of fractional discrete-time scalar systems with two delays. In Advances in the Theory and Applications of Non-integer Order Systems, (Lecture Notes in Electrical Engineering, 257), eds. W. Mitkowski, J. Kacprzyk, J. Baranowski. Berlin, Springer-Verlag, 2013, 53-66.
- [22] A. Ruszewski and M. Busłowicz: Practical and asymptotic stability of fractional discrete-time scalar systems with multiple delays. In Aktualne problemy automatyki i robotyki, eds. K.Malinowski, J. Józefczyk, J. Światek, Akademicka Oficyna Wydawnicza EXIT, Warszawa, 2014, 183-192.
- [23] J. Sabatier, O. P. Agrawal, J. A. T. Machado (eds.): Advances in Fractional Calculus, Theoretical Developments and Applications in Physics and Engineering. Springer, London (2007).
- [24] R. Stanisławski and K. J. Latawiec: Stability analysis for discrete-time fractional-order LTI state-space systems. Part I: New necessary and sufficient conditions for asymptotic stability. Bulletin of the Polish Academy of Sciences, 61 (2013), 353-361.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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