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Home  >  Volume 26 (March 2014)

7. Derivation of an Optimal Expression for Solution Matrices of a Class of Single – Delay Scalar Differential Equations by C. UkwuAnd E.J.D. Garba. Volume26, (March, 2014), pp28 – 35.
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This paper derived optimal expressions for solution matrices for single – delay autonomous linear differential equations with an accompanying corollary, on arbitrary intervals of length equal to the delay h , for non –negative time periods. The formulation and the development of the main result exploited an earlier work in [1] on the interval [0, 4h]. The proof was achieved using combinations of summation notations, integrals, change of variables technique, as well as the method of steps to obtain these matrices on successive intervals of length equal to the delay h. By exploiting above results, the paper obtained the solution of an initial function problem, as well as interrogated its smoothness disposition. The obtained results globally extend the time scope of applications of solution 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.