Simple stability conditions for linear positive discrete-time systems with delays

• Autorzy: Busłowicz M.
• Języki publikacji: EN

Abstrakty

EN

Simple new necessary and sufficient conditions for asymptotic stability of the positive linear discrete-time systems with delays in states are established. It is shown that asymptotic stability of the system is equivalent to asymptotic stability of the corresponding positive discrete-time system without delays of the same size. The considerations are illustrated by numerical examples.

Słowa kluczowe

EN

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

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2008
• Tom: Vol. 56, nr 4
• Strony: 325--328
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Busłowicz M.

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

Bibliografia

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• [2] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
• [3] M. Busłowicz, Robust Stability of Dynamical Linear Stationary Systems with Delays, Publishing Department of Technical University of Białystok, Warszawa–Białystok, 2000, (in Polish).
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• [7] S.-I. Niculescu, Delay Effects on Stability. A Robust Control Approach, Springer-Verlag, London, 2001.
• [8] M. Busłowicz, "Robust stability of scalar positive discretetime linear systems with delays”, Proc. Int. Conf. on Power Electronics and Intelligent Control 163, CD-ROM (2005).
• [9] M. Busłowicz, “Stability of positive singular discrete-time systems with unit delay with canonical forms of state matrices”, Proc. 12th IEEE Int. Conf. on Methods and Models in Automation and Robotics 215–218 (2006).
• [10] M. Busłowicz, “Robust stability of positive discrete-time linear systems with multiple delays with linear unity rank uncertainty structure or non-negative perturbation matrices”, Bull. Pol. Ac.: Tech. 55 (1), 1–5 (2007).
• [11] M. Busłowicz and T. Kaczorek, “Robust stability of positive discrete-time interval systems with time-delays”, Bull. Pol. Ac.: Tech. 52 (2), 99–102 (2004).
• [12] M. Busłowicz and T. Kaczorek, “Stability and robust stability of positive linear discrete-time systems with pure delay”, Proc. 10th IEEE Int. Conf. on Methods and Models in Automation and Robotics 1, 105–108 (2004).
• [13] M. Busłowicz and T. Kaczorek, “Recent developments in theory of positive discrete-time linear systems with delays – stability and robust stability”, Measurements, Automatics and Control 10, 9–12 (2004), (in Polish).
• [14] M. Busłowicz and T. Kaczorek, “Robust stability of positive discrete-time systems with pure delay with linear unity rank uncertainty structure”, Proc. 11th IEEE Int. Conf. on Methods and Models in Automation and Robotics 0169, CD-ROM (2005).
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• [18] T. Kaczorek, Polynomial and Rational Matrices, Applications in Dynamical Systems Theory, Springer-Verlag, London, 2006.
• [19] M. Busłowicz and T. Kaczorek, “Componentwise asymptotic stability and exponential stability of positive discrete-time linear systems with delays”, Proc. Int. Conf. on Power Electronics and Intelligent Control 160, CD-ROM (2005).
• [20] M. Busłowicz and T. Kaczorek, “Componentwise asymptotic stability and exponential stability of positive discrete-time linear systems with delays”, Measurements, Automatics and Control 7/8, 31–33 (2006), (in Polish).
• [21] T. Kaczorek, “Choice of the forms of Lyapunov functions for positive 2D Roesser model”, Int. J. Applied Math. and Comp. Sciences 17 (3), 471–475 (2007).
• [22] T. Kaczorek, “Practical stability of positive fractional discrete-time systems”, Bull. Pol. Ac.: Tech. 56 (2), (2008).