Advances in Difference Equations
Volume 2006 (2006), Article ID 80825, 13 pages
Representation of solutions of linear discrete systems with constant coefficients and pure delay
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.
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.