Multiple delayed linear difference equations with non-permutable matrix coefficients: The method of Z-transform

Abstract

In this paper, a system of nonhomogeneous linear difference equations is studied, characterized by any finite number of constant delays and linear components expressed through non-permutable matrices. An explicit representation of the solutions of multi-delayed linear difference equations is derived through the introduction of a multi-delayed perturbation using a multivariate determining function and the application of the Z-transform method. The necessity for the matrix of the non-delayed term to be invertible, a condition that had been mandated in recent research studies, is eliminated. The representation is suitable for theoretical as well as practical computations. © 2024, MTJPAM Turkey. All rights reserved.