Stability conditions of fractional discrete-time scalar systems with pure delay

• Autorzy: Ruszewski A.

Warianty tytułu

PL

Warunki stabilności skalarnych układów dyskretnych niecałkowitego rzędu z czystym opóźnieniem

• Języki publikacji: EN

Abstrakty

EN

In the paper the problem of stability of fractional discrete-time linear scalar systems with state space pure delay is considered. Using the classical D-decomposition method, the necessary and sufficient condition for practical stability as well as the sufficient condition for asymptotic stability are given.

PL

W pracy rozpatrzono problem stabilności liniowych skalarnych układów dyskretnych niecałkowitego rzędu z czystym opóźnieniem zmiennych stanu. Wykorzystując metodę podziału D podano warunek konieczny i wystarczający praktycznej stabilności oraz warunek wystarczający stabilności asymptotycznej.

Słowa kluczowe

EN

asymptotic stability; practical stability; fractional order; discrete-time linear system

PL

stabilność asymptotyczna; stabilność praktyczna; niecałkowity rząd; liniowy układ dyskretny

• Wydawca: Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów PIAP
• Czasopismo: Pomiary Automatyka Robotyka
• Rocznik: 2013
• Tom: R. 17, nr 2
• Strony: 340--344
• Opis fizyczny: CD, Bibliogr. 22 poz., wykr., wzory

Twórcy

autor

Ruszewski A.

• Faculty of Electrical Engineering, Białystok University of Technology, Poland,

Bibliografia

• 1. Das S., Functional Fractional Calculus for System Identification and Controls, Springer, Berlin 2008.
• 2. Busłowicz M., Stability of state-space models of linear continuous-time fractional order systems, „Acta Mechanica et Automatica”, Vol. 5, No. 2, 2011, 15-22.
• 3. Busłowicz M., Practical stability of scalar discrete-time linear systems of fractional order, [in:] Swierniak A., Krystek J. (Eds.), Automatyzacja procesów dyskretnych: teoria i zastosowania, Vol. 1, Gliwice 2012, 31-40 (in Polish).
• 4. Busłowicz M., Kaczorek T., Simple conditions for practical stability of linear positive fractional discrete-time linear systems, „International Journal of Applied Mathematics and Computer Science”, Vol. 19, No. 2, 2009, 263-269.
• 5. Debnath L., Recent applications of fractional calculus to science and engineering, „International Journal of Mathematics and Mathematical Sciences”, Vol. 54, 2003, 3413-3442.
• 6. Dzieliński A., Sierociuk D., Stability of discrete fractional state-space systems, „Journal of Vibration and Control”, Vol. 14, 2008, 1543-1556.
• 7. Dzieliński A., Sierociuk D., Sarwas G., Some applications of fractional order calculus, „Bulletin of the Polish Academy of Sciences: Technical Sciences”, Vol. 58, No. 4, 2010, 583-592.
• 8. Gryazina E.N., Polyak B.T., Tremba A.A., Ddecomposition technique state-of-the-art, „Automation and Remote Control”, Vol. 69, No. 12, 2008, 1991-2026.
• 9. Guermah S., Djennoune S., Bettayeb M., A New Approach for Stability Analysis of Linear Discrete-Time Fractional-Order Systems, [in:] Baleanu D. et al. (Eds.), New Trends in Nanotechnology and Fractional Calculus Applications, Springer, 2010, 151-162.
• 10. Kaczorek T., Practical stability of positive fractional discrete-time systems, „Bulletin of the Polish Academy of Sciences: Technical Sciences”, Vol. 56, No. 4, 2008, 313-317.
• 11. Kaczorek T., Selected Problems of Fractional Systems Theory, Publishing Department of Białystok University of Technology, Białystok 2009 (in Polish).
• 12. Kaczorek T., Selected Problems of Fractional Systems Theory, Springer, Berlin 2011.
• 13. Monje C., Chen Y., Vinagre B., Xue D., Feliu V., Fractional-order Systems and Controls, Springer-Verlag, London 2010.
• 14. Ostalczyk P., Epitome of the fractional calculus. Theory and its applications in automatics, Publishing Department of Technical University of Łódz, Łódz 2008 (in Polish).
• 15. Petras I., Stability of fractional-order systems with rational orders: a survey, „Fractional Calculus and Applied Analysis. An International Journal for Theory and Applications”, Vol. 12, 2009, 269-298.
• 16. Petras I., Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer, London 2011.
• 17. Podlubny I., Fractional Differential Equations, Academic Press, San Diego 1999.
• 18. Ruszewski A., Stability regions of closed loop system with time delay inertial plant of fractional order and fractional order PI controller, „Bulletin of the Polish Academy of Sciences: Technical Sciences”, Vol. 56, No. 4, 2008, 329-332.
• 19. Ruszewski A., Stabilization of inertial processes with time delay using fractional order PI controller, „Measurement Automation and Monitoring”, No. 2, 2010, 160-162.
• 20. Sabatier J., Agrawal O.P., Machado J.A.T. (Eds.), Advances in Fractional Calculus, Theoretical Developments and Applications in Physics and Engineering, Springer, London 2007.
• 21. Sheng H., Chen Y., Qiu T., Fractional Processes and Fractional-Order Signal Processing, Springer, London 2012.
• 22. Stanisławski R., Hunek W.P., Latawiec K.J., Finite approximations of a discrete-time fractional derivative, Proc. 16th IEEE Conference Methods and Models in Automation and Robotics, Miedzyzdroje, Poland 2011, 142-145.