Advances in Difference Equations
Volume 2006 (2006), Article ID 80825, 13 pages
doi:10.1155/ADE/2006/80825

Representation of solutions of linear discrete systems with constant coefficients and pure delay

J. Diblík1 and D. YA. Khusainov2

1Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Brno 602 00, Czech Republic
2Faculty of Cybernetics, Kiev National Taras Shevchenko University, Kiev 01033, Ukraine

Received 16 January 2006; Accepted 22 January 2006

Copyright © 2006 J. Diblík and D. YA. Khusainov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The purpose of this contribution is to develop a method for construction of solutions of linear discrete systems with constant coefficients and with pure delay. Solutions are expressed with the aid of a special function called the discrete matrix delayed exponential having between every two adjoining knots the form of a polynomial. These polynomials have increasing degrees in the right direction. Such approach results in a possibility to express initial Cauchy problem in the closed form.