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

• Autorzy: Mieloszyk E. , Milewska A. , Magulska M.
• 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,

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).