Compactness and convexity of cores of targets for neutral systems

Abstract

In this paper we prove the convexity and the compactness of the cores of targets for neutral control systems. We make use of a weak compactness argument; but in the crucial part where we establish the boundedness of the cores of the target we make use of the notion of asymptotic direction from Convex Set Theory. Let E n be n-dimensional Euclidean space. We prove that the core of the target H = L + E (where L = {x 6 E n | Mx = 0} , M is a constant m xn matrix and E is a compact, convex set containing 0) of the neutral systemis convex, and is compact if, and only if, the systemis Euclidean controllable.