Representation of solutions of delayed difference equations with linear parts given by pairwise permutable matrices via Z-transform

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摘要

In the present paper, a system of nonhomogeneous linear difference equations with any finite number of constant delays and linear parts given by pairwise permutable matrices is considered. Representation of its solution is derived in a form of a matrix polynomial using the Z-transform. So the recent results for one and two delays, and an inductive formula for multiple delays are unified. The representation is suitable for theoretical as well as practical computations.

论文关键词:Discrete system,Z-transform,Multiple delays,Matrix polynomial

论文评审过程:Received 13 April 2016, Revised 25 July 2016, Accepted 14 September 2016, Available online 28 September 2016, Version of Record 28 September 2016.

论文官网地址:https://doi.org/10.1016/j.amc.2016.09.019