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 equationdot{x}(t) = A(t)x(t) + intliminf{-h}limsup{0} dH(t,s)u(t+s)satisfied almost everywhere on t_{0},infty). If the systemdot{x}(t)=A(t)x(t)is uniformly asymptotically stable and the controlled systemdot{x}(t) = A(t)x(t) + intliminf{-h}limsup{0} dH(t,s)u(t+s)is proper then the system is null-controllable.