The Structure of Indices of Control Systems for Certain Single – Delay Autonomous Linear Systems with Problem Instances

Abstract

This paper investigated the structure of indices of control systems for single – delay autonomous linear systems on the interval [0, 4h] and on [0, ∞) for special coefficient matrix cases. It also provided a note on Euclidean controllability and application instances of the determination of their controllability dispositions. The development of the associated control index matrices exploited the continuity of these matrices for positive time periods, change of variables technique, the method of steps and backward continuation recursions 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. The structure could be gleaned and deciphered from the emerged sign convention and recognizable exponential integral ordering.