Robust stability of positive discrete-time linear systems with multiple delays with linear unity rank uncertainty structure or non-negative perturbation matrices

• Autorzy: Busłowicz M.
• Języki publikacji: EN

Abstrakty

EN

Simple necessary and sufficient conditions for robust stability of the positive linear discrete-time systems wit h delays with linear uncertainty structure in two cases: 1) unity rank uncertainty structure, 2) non-negative perturbation matrices, are established. The proposed condi-tions are compared wit h the suitable conditions for the standard systems. The considerations are illustrated by numerical examples.

Słowa kluczowe

EN

robust stability; linear system; discrete-time; positive; delays; linear uncertainty; unity rank uncertainty

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2007
• Tom: Vol. 55, nr 1
• Strony: 1--5
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Busłowicz M.

• Faculty of Electrical Engineering, Technical University of Białystok, 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] M. Busłowicz, "Robust stability of positive discrete-time systems wit h delay linear uncertainty structure", Prac. XV National Conf. Automatics 1, 179-182 (2005), (in Polish) .
• [4] M. Busłowicz, "Robust stability of scalar positive discrete-time linear systems wit h delays", Proc. Int. Conf. on Power Electronics and Intelligent Control 168, on CD-ROM (2005).
• [5] M. Busłowicz, "Stability of positive singular discrete-time systems wit h unit delay with canonical forms of state matrices", Proc. 12th IEEE Int. Conf. on Methods and Models in Automation and Robotics, (2006).
• [6] M. Busłowicz and T. Kaczorek, "Robust stability of positive discrete-time interval systems wit h time-delays", Bull. Pol. Ac.: Tech. 52 (2),99-102 (2004).
• [7] M. Busłowicz and T. Kaczorek, "Recent developments in theory of positive discrete-time linear systems wit h delays – stability and robust stability", Measurements, Automatics, Control 10, 9-12 (2004).
• [8] M. Busłowicz and T. Kaczorek, "Stability and robust stability of positive linear discrete-time systems wit h pure delay", Proc. 10th IEEE Int. Conf. on Methods and Models in Automation and Robotics 1, 105-108 (2004).
• [9] M. Busłowicz and T. Kaczorek, "Robust stability of positive discrete-time systems wit h pure delay with linear unity rank uncertainty structure", Proc. 11th IEEE Int. Conf. on Methods and Models in Automation and Robotics, on CD-ROM (2005).
• [10] M. Busłowicz and T. Kaczorek, "Component wise asymptotic stability and exponential stability of positive discrete-time linear systems wit h delays", Proc. Int. Conf. on Power Electronics and Intelligent Control 160, on CD-ROM (2005), Measurements, Automatics, Control 7(8), 31-33 (2006).
• [11] T. Kaczorek, "Stability of positive discrete-time systems wit h time-delay", Proc. 8th World Multiconference on Systemics, Cybernetics and Informatics, 321-324 (2004).
• [12] J. Ackermann, D. Kaesbauer, W. Sienel, and R. Steinhauser, Robust Control: Systems with Uncertain Physical Parameters, Springer- Verlag, London, 1994.
• [13] B.R. Barmish, New Tools for Robustness of Linear Systems, MacMillan Publishing Company, New York, 1994.
• [14] S.P. Bhattacharyya, H. Chapellat, and L.H. Keel, Robust Control: The Parametric .Approach, Prentice Hall PTR, New York, 1995.
• [15] S. Białas, Robust Stability of Polynomials and Matrices, Publishing Department of University of Mining and Metallurgy, Kraków, 2002, (in Polish).
• [16] M. Busłowicz, Stability of Linear Time-Invariant Systems with Uncertain Parameters, Publishing Department of Białystok Technical University, Białystok, 1997, (in Polish).