Euclidean null-controllability of linear systems with distributed delays in control

J. Klamka derives a necessary and sufficient condition for the relative controllability of linear systems with distributed delays in control. In this paper the author discusses the Euclidean null-controllability of system described by the equation
\dot{x}(t) = A(t)x(t) + \int\liminf{-h}\limsup{0} dH(t,s)u(t+s)
satisfied almost everywhere on [
t_{0},\infty
). If the system
\dot{x}(t)=A(t)x(t)
is uniformly asymptotically stable and the controlled system
\dot{x}(t) = A(t)x(t) + \int\liminf{-h}\limsup{0} dH(t,s)u(t+s)
is proper then the system is null-controllable.