Identyfikatory
Warianty tytułu
Stożkowe dyskretne układy Lapunowa ułamkowego rzędu
Języki publikacji
Abstrakty
The fractional discrete-time Lyapunov cone-systems are introduced. The necessary and sufficient conditions for being the cone system, reachability, controllability to zero and observability of the systems are established. The sufficient conditions for stability are given. The notion of the dual fractional Lyapunov cone-system is introduced and the relationship between the reachability and observability is given. The considerations are illustrated on the numerical example.
Praca przedstawia stożkowe dyskretne układy Lapunowa ułamkowego rzędu. Ustanowione są warunki konieczne i wystarczające bycia układem stożkowym, osiągalności, sterowalności do zera i obserwowalności dla tego typu układów. Przedstawione są również układy dualne do stożkowych dyskretnych układów Lapunowa ułamkowego rzędu oraz związek między osiągalnością i obserwowalnością. Rozważania są zilustrowane na przykładach numerycznych.
Wydawca
Czasopismo
Rocznik
Tom
Strony
47--52
Opis fizyczny
Bibliogr. 50 poz.
Twórcy
autor
- Warsaw University of Technology-Faculty of Electrical Engineering, Przybor@isep.pw.edu.pl
Bibliografia
- 1. Benvenuti L. and Farina L., A tutorial on positive realization problem, IEEE Trans. Autom. Control, vol. 49, No 5, 2004, pp. 651-664.
- 2. Bologna M. and Grigolini P., Physics of Fractal Operators. Springer-Verlag, New York, 2003.
- 3. Busłowicz M. and Kaczorek T., Reachability and minimum energy control of positive linear discrete-time systems with one delay, 12th Mediterranean Conference on Control and Automation, June 6-9, 2004, Kusadasi, Izmir, Turkey.
- 4. Dzieliński A. and Sierociuk D.. Stability of discrete fractional order state-space systems. In Proceedings of 2nd IFAC Workshop on Fractional Differentiation and its Applications. IFAC FDA’06, 2006.
- 5. Farina L. and Rinaldi S., Positive Linear Systems; Theory and Applications, J. Wiley, New York 2000.
- 6. Ferreira N.M.F. and Machado I.A.T., Fractional-order hybrid control of robotic manipulators. Proc. 11th Int. Conf. Advanced Robotics, ICAR’2003, Coimbra, Portugal, 2003, pp. 393-398.
- 7. Gałkowski K., Fractional polynomials and nD systems. Proc IEEE Int. Symp. Circuits and Systems, ISCAS’2005, Kobe, Japan, CD-ROM.
- 8. Kaczorek T., Positive 1D and 2D systems, Springer Verlag, London 2001.
- 9. Kaczorek T., Vectors and Matrices in Automation and Electrotechnics, Wydawnictwo Naukowo-Techniczne, Warszawa 1998 (in Polish).
- 10. Kaczorek T., New reachability and observability tests for positive linear discrete-time systems, Bull. Pol. Acad. Sci. Techn. vol. 55, No. 1, 2007.
- 11. Kaczorek T., Realization problem for positive discrete-time systems with delay, System Science, vol. 30, No. 4, 2004, pp.117-130.
- 12. Kaczorek T., Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs, Int. J. Appl. Math. Comp. Sci. 2006, vol. 16, No. 2, pp. 101-106.
- 13. Kaczorek T., A realization problem for positive continuous-time systems with reduced number of delays, Int. J. Appl. Math. Comp. Sci. 2006, vol. 16, No. 3, pp. 101-117.
- 14. Kaczorek T., Positive discrete-time linear Lyapunov systems, The 15th Mediterranean Conference of Control and Automation – MED 2007, 27-29 June, Athens.
- 15. Kaczorek T., Stability of positive discrete-time systems with time-delay, The 8th World Multi-Conference on Systemics, Cybernetics and Informatics, July 18-21, 2004 ~ Órlando, Florida, USA.
- 16. Kaczorek T., Reachability and controllability to zero of positive fractional discrete-time systems, Machine Intelligence and Robotics Control, vol. 6, No. 4, 2007.
- 17. Kaczorek T., Reachability and controllability to zero tests for standard and positive fractional discrete-time systems, Submitted to Journal European Systems Analysis. 2007.
- 18. Kaczorek T., Reachability and controllability to zero of cone fractional linear systems, Archives of Control Sciences, vol. 17, 2007, No.3, pp. 357-367.
- 19. Kaczorek T., Computation of realizations of discrete-time cone-systems, Bulletin of the Polish Academy of Sciences Technical Sciences, vol. 54, No. 3, 2006.
- 20. Kaczorek T. and Busłowicz M., Minimal realization problem for positive multivariable linear systems with delay, Int. J. Appl. Math. Comp. Sci. 2004, vol. 14, No. 2, pp. 181-187.
- 21. Kaczorek T. and Busłowicz M., Recent developments in theory of positive discrete-time linear systems with delays – stability and robust stability, Pomiary, Automatyka, Kontrola, No 9, 2004, pp. 9-12
- 22. Kaczorek T. and Busłowicz M., Recent developments in theory of positive discrete-time linear systems with delays – reachability, minimum energy control and realization problem Pomiary, Automatyka, Kontrola, No 9, 2004, pp. 12-15.
- 23. Kaczorek T. and Przyborowski P., Positive continues-time linear Lyapunov systems, Proceedings of The International Conference on Computer as a Tool EUROCON 2007, 9-12 September, Warsaw , pp. 731-737.
- 24. Kaczorek T. and Przyborowski P., Positive continuous-time linear time-varying Lyapunov systems, Proceedings of The XVI International Conference on Systems Science, 4-6 September 2007, Wroclaw – Poland , vol. I, pp. 140-149.
- 25. Kaczorek T. and Przyborowski P., Continuous-time linear Lyapunov cone-systems, Proceedings of The 13th IEEE IFAC International Conference on Methods and Models in Automation and Robotics, 27 - 30 August 2007, Szczecin – Poland, pp. 225-229.
- 26. Kaczorek T. and Przyborowski P., Reachability, controllability to zero and observability of the positive discrete-time Lyapunov systems, The Control and Cybernetics Journal, 2007 (in press).
- 27. Kaczorek T. and Przyborowski P., Positive discrete-time linear Lyapunov systems with delays, Proceedings of The International Workshop "Computational Problems of Electrical Engineering September 14th-16th, 2007, Wilkasy, Poland, Electrical Review (Przegląd Elektrotechniczny), 2k/2007, pp. 12-15.
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- 43. Przyborowski P., Positive Fractional Discrete-time Lyapunov Systems, Submitted to Archives of Control Sciences, 2008.
- 44. Reyes-Melo M.E., Martinez-Vega J.J., Guerrero-Salazar C.A. and Ortiz-Mendez U., Modelling and relaxation phenomena in organic dielectric materials. Application of differential and integral operators of fractional order. J. Optoel. Adv. Mat. Vol. 6, no. 3, 2004, pp. 1037-1043.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
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