Euclidean controllability of linear delay systems with limited controls

Abstract

For linear delay systems with limited controls the notion of a proper control system is introduced. If the uncontrolled system x(t) = Ax(t) + Bx(t - h) is uniformly asymptotically stable and the control equation x(t) = Ax(t) + Bx(t-) + Cu(t) is proper, then the control system is Euclidean null-controllable. It is noted that controllability is equivalent to the system being proper for delay systems with unlimited power.