Abstract: This paper derived the structure of the indices of control systems for a class of single – delay autonomous linear differential equations 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 part of an existing result on the interval a compact interval. The derivation of the associated solution matrices exploited the continuity of these matrices for positive time periods, the method of steps and backward continuation recursions to obtain these matrices on successive intervals of length equal to the delay h. The proof was achieved using combinations of integrals, summation notations, change of variables technique integrals, as well as the method of steps to obtain these matrices on successive intervals of length equal to the delay h. The indices were derived using the stage – wise algorithmic format, starting from the right – most interval of length h. This theorem globally extends the time scope of applications of these matrices to the solutions of terminal function problems and rank conditions for controllability and cores of targets.
Keywords: Structure, Indices, control systems, Method of steps, Change of variables.
Title: The Structure of Indices of Control Systems for Single – Delay Autonomous Scalar Differential Equations
Author: Ukwu Chukwunenye
International Journal of Mathematics and Physical Sciences Research
ISSN 2348-5736 (Online)
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