Euclidean controllability of linear delay systems with limited controls

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