Optimal Expressions for Solution Matrices of Single – Delay Differential Systems.

Abstract

This paper derived optimal expressions for solution matrices of single – delay autonomous linear differential systems on any given interval of length equal to the delay h for non –negative time periods. The formulation and the development of the theorem exploited an earlier work Ukwu (2013b) on the interval [0, 4h]. The proofs were achieved using ingenious combinations of summation notations, multiple product notations and integrals, as well as the method of steps to obtain these matrices on successive intervals of length equal to the delay h. This theorem globally extends the time scope of applications of these matrices to the solutions of initial function problems, rank conditions for controllability and cores of targets, constructions of controllability Grammians and admissible controls for transfers of points associated with controllability problems.