Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The notions of invariant, decoupling and blocking zeros are extended to the fractional linear systems. It is shown that: 1) The zeros are closely connected with the controllability and observability of the linear systems and their transfer functions matrices. 2) The state vector of the fractional system for any input and zero initial conditions is independent of the input decoupling zeros of the system. 3) The output of the fractional system for any input and zero initial conditions is independent of the input-output decoupling zeros of the system.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
44--48
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
autor
- Faculty of Electrical Engineering, Białystok University of Technology, ul. Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
- 1. Antsaklis E., Michel A. (2006), Linear Systems, Birkhauser, Boston.
- 2. Busłowicz M. (2008), Stability of linear continuous-time fractional order systems with delays of the retarded type, Bull. Pol. Acad. Sci. Tech., 56(4). 319-324.
- 3. Dzieliński A., Sierociuk D. (2008), Stability of discrete fractional order state-space systems, Journal of Vibrations and Control, 14(9-10), 1543-1556.
- 4. Dzieliński A., Sierociuk D., Sarwas G. (2009), Ultracapacitor parameters identification based on fractional order model, Proc. European Control Conference, Budapest, Hungary, 196-200.
- 5. Farina L., Rinaldi S. (2000), Positive Linear Systems: Theory and Applications, J. Wiley & Sons, New York.
- 6. Gantmacher, F.R. (1988), The theory of matrices, AMS Chelsea Publishing, Rhode Island.
- 7. Kaczorek T. (1993), Linear Control Systems, vol. 1, J. Wiley, New York.
- 8. Kaczorek T. (2002), Positive 1D and 2D Systems, Springer-Verlag, London.
- 9. Kaczorek T. (2008), Practical stability of positive fractional discretetime linear systems, Bull. Pol. Acad. Sci. Tech., 56(4), 313-317.
- 10. Kaczorek T. (2009), Asymptotic stability of positive fractional 2D linear systems, Bull. Pol. Acad. Sci. Tech., 57(3), 289-292.
- 11. Kaczorek T. (2010), Decoupling zeros of positive discrete-time linear systems, Circuits and Systems, 1, 41-48.
- 12. Kaczorek T. (2011a), Positive electrical circuits and their reachability, Archives of Electrical Engineering, 60(3), 283-301.
- 13. Kaczorek T. (2011b), Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. Circuits and Systems, 58(6), 1203-1210.
- 14. Kaczorek T. (2011c), Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica, 5(2), 42-51.
- 15. Kaczorek T. (2011d), Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
- 16. Kaczorek T. (2013a), Constructability and observability of standard and positive electrical circuits, Electrical Review, 89(7), 132-136.
- 17. Kaczorek T. (2013b), Decoupling zeros of positive electrical circuits, Archives of Electrical Engineering, 62(4), 553-568.
- 18. Kaczorek T. (2017a), Invariant, decoupling and blocking zeros of positive linear electrical circuits with zero transfer matrices, Circuits, Systems, and Signal Processing, 36(11), 4716-4728.
- 19. Kaczorek T. (2017b), Specific properties of invariant, decoupling and blocking zeros of positive linear electrical circuits with zero transfer matrices, Proc. of SPIE, 104451C.
- 20. Kaczorek T., Rogowski K. (2015), Fractional Linear Systems and Electrical Circuits, Studies in Systems, Decision and Control, vol. 13, Springer.
- 21. Kailath T. (1980), Linear systems, Prentice Hall, Englewood Cliffs, New York.
- 22. Kalman R. (1960), On the general theory of control systems, Proc. First Intern. Congress on Automatic Control, London, UK: Butterworth, 481-493.
- 23. Kalman R. (1963), Mathematical description of linear systems, SIAM J. Control, 1(2), 152-192.
- 24. Rosenbrock H. (1970), State-space and multivariable theory, J. Wiley, New York.
- 25. Tokarzewski J. (2011a), Finite zeros of positive linear discrete-time systems, Bull. Pol. Acad. Sci. Tech., 59(3), 287-292.
- 26. Tokarzewski J. (2011b), Finite zeros of positive continuous-time systems, Bull. Pol. Acad. Sci. Tech., 59(3), 293-298.
- 27. Valcher M.E. (1977), On the initial stability and asymptotic behaviour of 2D positive systems, IEEE Trans. on Circuits and Systems – I, 44(7), 602-613.
- 28. Wolovich W.A. (1974), Linear Multivariable Systems, SpringerVerlag, New York.
Uwagi
2. The studies have been carried out in the framework of work No. S/WE/1/2016 and financed from the funds for science by the Polish Ministry of Science and Higher Education.
2. Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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