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Warianty tytułu
Języki publikacji
Abstrakty
In the paper the positive fractional discrete-time linear systems with delay described by the state equations are considered. The solution to the state equations is derived using the Z transform. Necessary and sufficient conditions are established for the positivity, reachability and controllability to zero for fractional systems with one delay in state. The considerations are illustrated by an example.
Rocznik
Tom
Strony
43--47
Opis fizyczny
Bibliogr. 12 poz., rys.
Twórcy
autor
- Białystok Technical University, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, w trzasko@pb.edu.pl
Bibliografia
- [1] Busłowicz M., Kaczorek T., "Reachability and minimum energy control of positwe discrete-time linear systems with multiple delays in state and contror. In: 44th IEEE CDC-ECC05, Sevilla 2005, Spain.
- [2] Busłowicz M., "Explicit solution of discrete-delay equations", Foundations of Control Engineering, vol. 7, no. 2,1982, pp. 67-71.
- [3] Kaczorek L, Positive ID and 20 Systems, Springer-Verlag, London 2002.
- [4] Kaczorek T., "Reachability and controllability to zero of positive fractional discrete-time systems", Machine Intelligence and Robotic Control, vol 6, no. 4, 2007.
- [5] Lazarevic M. P., "Finite time stability analysis of PD fractional control of robotic time-delay systems", Mechanics Research Communications 33, 2006, pp. 269-279.
- [6] Matignon D., d'Andre'a-Novel B., "Some results on controllability and observability of finite-dimensional fractional differential systems". In: Proceedings of the Computational Engineering in Systems and Application, France 1996, vol. 2, IMACS, IEEE-SMC, pp. 952-956.
- [7] Miller K. S., Ross B., Ań Introduction to the fractional calculus and fractional differential equations, Willey, New York, 1993.
- [8] Podlubny L, "Matrix approach to discrete fractional calculus", An International Journal for Theory and Applications, vol. 3, no. 4, 2000, pp. 359-386.
- [9] Trzasko W., Kociszewski R., "Controllability of positive discrete-time systems with delays in state and control". In: Proceedings 15th National Conference of Automatics, Warsaw, 2005, vol. 2, pp. 127-130 (in Polish).
- [10] Zhang X., „Some results of linear fractional order time-delay system", Appl. Math. Comput, 2007 (in press).
- [11] Xie G., Wang L, "Reachability and controllability of positive linear discrete-time systems with time-delays". In: Positive Systems (Benvenuti, De Santis and Farina (Eds.), Springer-Verlag, Berlin Heidelberg, 2003, pp. 377-384.
- [12] Blas M. Vinagre, "Fractional Calculus Fundamentals". Tutorial Workshop #2. Fractional Calculus Applications in Automatic Control and Robotics, 41st IEEE Conference on Decision and Control, Las Vegas, 2002.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUJ5-0020-0017