Bulletin of the Australian Mathematical Society

Table of Contents - 1989 - Volume 39, Issue 03  

Research Article

Compactness and convexity of cores of targets for neutral systems

Anthony N. Ekea1

a1 Department of Mathematics, University of Nigeria, Nsukka, Nigeria.

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 boundeduess of the cores of the target we make use of the notion of asymptotic direction from convex Set Theory. Let En be n-dimensional Euclidean space. We prove that the core of the target H = L + E (where L = {x xs2208 En | Mx = 0}, M is a constant in m × n matrix and E is a compact, convex set containing 0) of the neutral system

S0004972700003373_eqnU1

is convex, and is compact if, and only if, the system

S0004972700003373_eqnU2

is Euclidean controllable.

(Received July 21 1988)