The Structure of Transition Matrices for Certain Single Delay Systems and Application Instances

Abstract

This paper investigated the expressions and structure of the transition matrices for single - delay autonomous linear systems on the interval [0, 4h]. Sequel to this, the paper obtained the structure of the transition matrices when any of the system’s coefficient matrices is diagonal. The development of the transition matrices exploited the continuity of these matrices for positive time periods and the method of steps to obtain these matrices on successive intervals of length equal to the delay h. The paper also discussed the analytic disposition of these matrices as well as provided elucidating application instances to the solutions of initial function problems.