General Solution of Linear Planar Weakly Delayed Discrete Systems with Multiple Delays and with a Singular Matrix of Non-delayed Terms

Abstract

A planar weakly delayed linear discrete system with multiple delays is considered. Assuming that the conditions for weakly delayed systems are fulfilled, the general solution of the system is constructed in the previously not considered case of the matrix of nondelayed terms having a single nonzero eigenvalue with the second one being zero. Then, there exists a non-delayed planar discrete system that, for all sufficiently large values of the independent variable, has the same general solution. New findings are illustrated with an example and discussed in relation to the previously known investigations. The formulas derived can be useful in digital signal processing.