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

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.