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## Bulletin of the Polish Academy of Sciences. Technical Sciences

Tytuł artykułu

### Non-classical operational calculus applied to certain linear discrete time-system

Autorzy Mieloszyk, E.  Milewska, A.  Magulska, M.
Treść / Zawartość http://journals.pan.pl/dlibra/journal/95347
Warianty tytułu
Języki publikacji EN
Abstrakty
 EN In the paper there bas been made an advantage of the non-classical operational calculus to determination of the response of the certain discrete time-systems. The Z-transform is often used to analysis of the stationary discrete time-systems. However, the use of the Z-transform to determination of the response especially of the non-stationary discrete time-systems is doubtful or may cause complications. This method leads to differential equa-tions of n-th order of variable coefficients, whose solutions are very difficult or impossible. The non-classical operational calculus ran be used to analysis both of the stationary and non-stationary discrete time-systems. The presented method with the use of the Heaviside operator soon leads to the target without unnecessary differential equations.
Słowa kluczowe
 EN discrete-time system   Z-transform   non-classical operational calculus   Heaviside operator   analysis of the discrete time-system
Wydawca Polska Akademia Nauk, Wydział IV Nauk Technicznych
Czasopismo Bulletin of the Polish Academy of Sciences. Technical Sciences
Rocznik 2006
Tom Vol. 54, nr 4
Strony 449--455
Opis fizyczny Bibliogr. 8 poz., rys., tab.
Twórcy
 autor Mieloszyk, E. autor Milewska, A. autor Magulska, M. Faculty of Applied Physics and Applied Mathematics, Gdańsk University of Technology, 11/12 Narutowicza St., 80-952 Gdańsk, Poland, e.mieloszyk@wp.pl
Bibliografia
[1] E.I. Jury, Theory and Application of the Z-transform method, WNT, Warszawa, 1970, (in Polish).
[2] J. Kudrewicz, The Z-transform and the Difference Equations, PWN, Warszawa, 2000, (in Polish).
[3] R. Bittner, “Operational calculus in linear spaces”, Studia Math. 20, 1-18 (1961).
[4] R. Bittner, Operational Calculus in Groups, PWN, Warszawa, 1992, (in Polish).
[5] E. Mieloszyk, Generalized Dynamical Systems Expressed in Terms of Operational Calculus, Publishing House of IMP Polish Academy of Sciences, Gdańsk, 2003, (in Polish).
[6] E. Mieloszyk, “Application of the operational calculus in solving partial difference equation”, Acta Math. Hung. 48, 117–130 (1986).
[7] I. Ko´zniewska, Recurrent Equations, PWN, Warszawa, 1972, (in Polish).
[8] E. Mieloszyk and A. Milewska, “Application of the operational calculus to eigenvalue problem for some difference equation of 2nd order”, Mathematical Exercises of Gdansk University of Technology XVII, 123–134 (1996).
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