Generalized regular differential systems with distributed delay

• Autorzy: Kalogeropoulos G. I. , Kossak O. , Pantelous A. A.
• Języki publikacji: EN

Abstrakty

EN

In this paper, a special class of generalized regular differential delay systems with constant coefficients is extensively studied. In practice, these kinds of systems can model the size of a population or the value of an investment. By considering the regular Matrix Pencil approach we finally decompose it into two subsystems, whose solutions are obtained. Moreover, since the initial function is given, the corresponding initial value problem is uniquely solvable. Finally, an illustrative application is presented using dde23 MatLab (m-) file based on the explicit Runge-Kutta method.

Słowa kluczowe

EN

matrix pencil theory; generalized regular delay systems

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Systems Science
• Rocznik: 2008
• Tom: Vol. 34, no 1
• Strony: 15--22
• Opis fizyczny: Bibliogr. 17 poz., wykr.

Twórcy

autor

Kalogeropoulos G. I.

autor

Kossak O.

autor

Pantelous A. A.

• Department of Mathematics, University of Athens, Panepistimiopolis, 157 84 Athens, Greece,

Bibliografia

• [1] Bellmann R., Cooke K.L., Differential-Difference Equations, Academic Press, New York 1963.
• [2] Breda D., Maset S., Vermiglio R., Computing the characteristic roots for delay differential equations, IMA Journal of Numerical Analysis, Vol. 24, 2004, pp. 1-19.
• [3] Breda D., Solution operator approximations for characteristic roots of delay differential equations, Applied Numerical Mathematics, Vol. 56, 2006, pp. 305-317.
• [4] Campbell S.L., Singular Systems of Differential Equations, Pitman, San Francisco, Vol. 1, Vol. 2, 1980, 1982.
• [5] Dai L., Singular Control Systems, Springer-Verlag, Berlin-Heidelberg 1989.
• [6] Diekmann O., Van Gils S.A., Verduyn Lunel S.M., Walther H.O., Delay Equations (Functional-, Complex-, and Nonlinear-Analysis), Springer-Verlag, New York 1995.
• [7] Gantmacher R.F., The Theory of Matrices, Vol. I and II, Chelsea, New York 1977.
• [8] Hale J.K., Theory of Functional Differential Equations, Springer-Verlag, New York 1977.
• [9] Hale J.K., Verduyn Lunel S.M., Introduction to Functional Differential Equations, Springer-Verlag, New York 1993.
• [10] Kalogeropoulos G.I., Matrix Pencils and Linear Systems, PhD Thesis, City University, London 1985.
• [11] Kalogeropoulos G.I., Stratis I.G., On generalized linear regular delay systems, J. Math. Anal. Appl., Vol. 237, 1999, pp. 505-514.
• [12] Karcanias N., Matrix pencil approach to geometric systems theory, Proc. IEE, Vol. 126, 1979, pp. 585-590.
• [13] Karcanias N., Hayton G.E., Generalized autonomous differential systems, algebraic duality, and geometric theory, Proc. IFAC VIII, Triennial World Congress, Kyoto, Japan, 1981.
• [14] Kytagias D., An Algorithmic Method of Computation of the Reduced set of Quadratic Plücker Relations and Applications in Feedback Problems of Regular and Singular Control Systems, PhD Thesis, University of Athens, Greece, 1993.
• [15] Shampine L.F., Thompson S., Solving Delay Differential Equations in MatLab, Applied Numerical Mathematics, Vol. 37, 2001, pp. 441-458.
• [16] Van Dooren P., Reducing Subspaces: Definitions, Properties, and Algorithms, Matrix Pencils, Lecture Notes in Mathematics, Vol. 973, Springer-Verlag, Berlin-New York 1983.
• [17] Wei J., Eigenvalue and stability of singular differential delay systems, J. Math. Anal. Appl., Vol. 297, 2004, pp. 305-316.