Cores of Euclidean Targets for Single-Delay Autonomous Linear Neutral Control Systems

Abstract

This paper established the convexity, compactness and subspace properties of cores of Euclidean targets for single-delay autonomous linear neutral control systems.The paper also revealed that the problem of controlling any initial endowment to a prescribed target and holding it there reduces to that of controlling the endowment to the core of the target with no further discussion about the problem as soon as this core is attained, since the right kind of behavior has been enforced on the initial endowment. The proof of the boundedness relied on the notion of asymptotic directions and other convex set properties, while that of the closedness appropriated a weak compactness argument.