General Solution of a Planar Linear Discrete System with a Weak Single Delay in the Case of Single Zero Eigenvalue of the Matrix of Nondelayed Terms

Abstract

Considered are linear planar discrete systems with a single delay. It is shown that their solutions can be expressed by explicit formulas given that the matrix of the linear non-delayed terms has two real eigenvalues with exactly one of them equaling zero and that the coefficients of the involved matrices depending on time satisfy certain conditions known for weakly delayed discrete systems with constant coefficients. Formulas derived can be useful in processing digital signals.