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

Josef Diblík and Blanka Morávková

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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 Δx(k) = Bx(k − m) + Cx(k − n) + f(k), where m, n ∈ ℕ, m ≠ n, are fixed, k = 0, …, ∞, B = (bij), C = (cij) are constant r × r matrices, f is a given r × 1 vector, and x is an r × 1 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.

Date: 2014
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https://doi.org/10.1155/2014/320476

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:320476

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