Stabilization of positive continuous-time linear systems with delays by state feedback

• Autorzy: Kaczorek T.

Warianty tytułu

PL

Stabilizacja dodatnich ciągłych układów liniowych z opóźnieniami za pomocą sprzężeń zwrotnych od wektora stanu

• Konferencja: 13th International Conference Computer Systems Aided Science, Industry and Transport "TRANSCOMP 2009"
• Języki publikacji: EN

Abstrakty

EN

The problem of finding a gain matrix of the state-feedback of positive continuoustime linear system with delays such that the closed-loop system is positive and asymptotically stable is formulated and solved. Necessary and sufficient conditions for the solvability of the problem are established. A procedure for computation of the gain matrix is given. It is shown that the asymptotic stability of the positive systems is independent of the number and values of the delays and it depends only on the sum of the state matrices.

PL

W pracy sformułowano i rozwiązano zadanie doboru macierzy sprzężeń zwrotnych dodatniego układu ciągłego tak, aby układ zamknięty był dodatni i stabilny asymptotycznie. Podano warunki konieczne i wystarczające na istnienie rozwiązania tego zadania oraz procedurę wyznaczania macierzy sprzężeń zwrotnych. Wykazano, że stabilność asymptotyczna układów dodatnich z opóźnieniami nie zależy od liczby i wielkości tych opóźnień, a zależy tylko od sumy macierzy stanu tego układu.

Słowa kluczowe

EN

positive continuous-time; system with delays; stability

PL

dodatni układ ciągły; system z opóźnieniem; stabilizacja

• Wydawca: Sieć Badawcza Łukasiewicz - Poznański Instytut Technologiczny
• Czasopismo: Logistyka
• Rocznik: 2009
• Tom: nr 6
• Strony: CD--CD
• Opis fizyczny: -pełny tekst, Bibliogr. 20 poz.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• 1. Busłowicz M., Robust stability of positive discrete-time linear systems with multiple delays with unity rank uncertainty structure or non-negative perturbation matrices, Bull. Pol. Acad. Techn. Sci. Vol. 55, No. 1, 2007, 347-350.
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• 5. Busłowicz M., Stability of positive singular discrete-time system with unit delay with canonical forms of state matrices, Proc. 12th IEEE int. Conf. on Methods and Models in Automation and Robotics, Międzyzdroje 2006, pp. 215-218.
• 6. Busłowicz M., Robust stability of positive discrete-time linear systems with multiple delays with linear unit rank uncertainty structure or non-negative perturbation matrices, Bull. Pol. Acad. Sci. Tech., Vol. 52, No. 2, 2004, pp. 99-102.
• 7. Busłowicz M. and Kaczorek T., Robust stability of positive discrete-time interval systems with time-delays, Bull. Pol. Acad. Sci. Tech., Vol. 55, No. 1, 2007, pp. 1-5.
• 8. Busłowicz M. and Kaczorek T., Stability and robust stability of positive discrete-time systems with pure delays, Proc. of the 10th IEEE Int. Conf. on Methods and Models in Automation and Robotics, Międzyzdroje 2004, Vol. 1, pp.105-108.
• 9. Busłowicz M. and Kaczorek T., Robust stability of positive discrete-time systems with pure delays with linear unit rank uncertainty structure, Proc. of the 11th IEEE Int. Conf. on Methods and Models in Automation and Robotics, Międzyzdroje 2005, Paper 0169 (on CD-ROM).
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• 18. Kaczorek T. Stability of positive continuous-time linear systems with delays. Bull.Pol.Acad.Sci.Techn.vol.57,No.4,2009.
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