Duality between Initial and Terminal Function Problems

Abstract

This paper successfully investigated the topological duality between initial and terminal function problems with respect to single-delay autonomous linear control systems using the expressions for the solution matrices and indices of control systems developed and proved in Ukwu and Garba [2014a, c] for single – delay autonomous linear systems, as well as the general variation of constants formula for the relevant systems. The paper obtained independent proofs that the solution matrices and the indices of control systems are analytic almost everywhere and differentiable except at a single point. The proofs were achieved using an algorithm involving key transformations from one problem to the other, effectively establishing that the results from one problem can be realized from the other.