Open Access

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

Advances in Difference Equations20062006:080825

https://doi.org/10.1155/ADE/2006/80825

Received: 16 January 2006

Accepted: 22 January 2006

Published: 7 June 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.

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Authors’ Affiliations

(1)
Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology
(2)
Faculty of Cybernetics, Kiev National Taras Shevchenko University

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Copyright

© J. Diblík and D.Ya. Khusainov 2006

This article is published under license to BioMed Central Ltd. 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.