Representation of the solutions of linear discrete systems with constant coefficients and two delays
type: Item
instance of: scholarly article
title: Representation of the solutions of linear discrete systems with constant coefficients and two delays
zbMATH Open document ID: 1463.39002
DOI: 10.1155/2014/320476
author: Josef Diblík
author: Blanka Morávková
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: 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 \(\Delta x(k)=Bx(k-m)+Cx(k-n)+f(k)\), where \(m,n\in\mathbb N\), \(m\neq n\), are fixed, \(k=0,\dots,\infty\), \(B=(b_{ij})\), \(C=(c_{ij})\) are constant \(r\times r\) matrices, \(f\) is a given \(r\times1\) vector, and \(x\) is an \(r\times1\) 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.
Mathematics Subject Classification ID: 39A06
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 7022165
zbMATH Keywords: initial problems
zbMATH Keywords: linear discrete systems
zbMATH Keywords: delays
Wikidata QID: Q59036144
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/320476
OpenAlex ID: W1978711257
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description: scientific article; zbMATH DE number 7022165