Robust stability of positive discrete-time interval systems with time-delays

• Autorzy: Busłowicz M. , Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

Necessary and sufficient conditions for robust stability of the positive discrete-time interval system with time-delays are established. It is shown that this system is robustly stable if and only if one well defined positive discrete-time system with time-delays is asymptotically stable. The considerations are illustrated by numerical example.

Słowa kluczowe

EN

robust stability; linear system; positive system; interval system; discrete-time; time-delay

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2004
• Tom: Vol. 52, nr 2
• Strony: 99--102
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Busłowicz M.

• Faculty of Electrical Engineering, Białystok Technical University, 45d Wiejska St., 15–351 Białystok, Poland

autor

Kaczorek T.

• Faculty ofE lectrical Engineering, Białystok Technical University, 45d Wiejska St., 15–351 Białystok, Poland

Bibliografia

• [1] L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley, New York (2000).
• [2] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London (2002).
• [3] T. Kaczorek, “Some recent developments in positive systems”, Proc. 7th Conf. on Dynamical Systems: Theory and Applications, pp. 25–35, Łódź, (2003).
• [4] M. Busłowicz and T. Kaczorek, “Reachability ofp ositive discrete-time systems with one time-delay”, Proc. National Conf. on Automation of Discrete Processes, Zakopane (2004), (in Polish).
• [5] G. Xie and L. Wang, “Reachability and controllability of positive linear discrete-time systems with time-delays”, in: Positive Systems, pp. 377–384, eds: L. Benvenuti, A. De Santis, L. Farina, Springer-Verlag, Berlin (2003).
• [6] T. Kaczorek and M. Busłowicz, “Minimal energy control of positive discrete-time systems with one time delay”, Proc. National Conf. on Automation of Discrete Processes, Zakopane (2004), (in Polish).
• [7] M. Busłowicz, “Robust stability ofdynamic al linear timeinvariant systems with delays”, Ser. Monographs of Committee of Automation and Robotics of Polish Academy of Sciences, vol. 1, Publishing Department ofT echnical University of Białystok, Warszawa-Białystok (2000), (in Polish).
• [8] H. Górecki, S. Fuksa, P. Grabowski, A. Korytowski, Analysis and Synthesis of Time Delay Systems, J. Wiley, Chichester (1989).
• [9] H. Górecki and A. Korytowski, Advances in Optimization and Stability Analysis of Dynamical Systems, Publishing Department ofUniv ersity ofM ining and Metallurgy, Kraków (1993).
• [10] J. E. Marshall, H. Górecki, K. Walton and A. Korytowski, Time-delay Systems Stability and Performance Criteria with Applications, Ellis Horwood, Chichester (1992).
• [11] S. Białas, Robust Stability of Polynomials and Matrices, Publishing Department ofUniv ersity ofM ining and Metallurgy, Kraków (2002), (in Polish).
• [12] M. Busłowicz, Stability of Linear Time-invariant Systems with Uncertain Parameters, Publishing Department of Technical University ofBiałyst ok, Białystok 1997, (in Polish).
• [13] T. Kaczorek, “Stability ofp ositive discrete-time systems with time-delay”, Proc. 12th Mediteranean Conf. Control and Automation June 6-9, 2004, Kasadasi, Turkey.
• [14] A.V. Kuncevitch and V. M. Kuncevitch, “Robust stability ofst ationary and nonstationary linear discete-time systems”, Avtomatica 3, 3–10 (1992).
• [15] B. Shafai, K. Perev, D. Cowley and Y. Chehab, “A necessary and sufficient conditions for the stability of nonnegative interval discrete systems”, IEEE Trans. Automat. Control 36, 742–747 (1991).
• [16] S. P. Bhattacharyya, H. Chapellat and L. H. Keel, Robust Control: The Parametric Approach, Prentice Hall, New York (1995).