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Abstract and Applied Analysis
Volume 2014, Article ID 320476, 19 pages
http://dx.doi.org/10.1155/2014/320476
Research Article

Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays

1Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, 602 00 Brno, Czech Republic
2Department of Mathematics, Faculty of Electrical Engineering, Brno University of Technology, 616 00 Brno, Czech Republic

Received 5 September 2013; Accepted 4 October 2013; Published 16 April 2014

Academic Editor: Miroslava Růžičková

Copyright © 2014 Josef Diblík and Blanka Morávková. 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 paper is to develop a method for the construction of solutions to initial problems of linear discrete systems with constant coefficients and with two delays where , are fixed, , , are constant matrices, is a given vector, and is an unknown vector. Solutions are expressed with the aid of a special function called the discrete matrix delayed exponential for two delays. Such approach results in a possibility to express an initial Cauchy problem in a closed form. Examples are shown illustrating the results obtained.