Abstract
Necessary and sufficient conditions of pointwise completeness at time t1 (i.e. no component of the n-dimensional state vector should be equal to zero at time i, for all possible choices of the initial functions) of any system of the form x(t)= Ax(t) + Bx(t-h) are given. It has been shown that if the linear time-invariant delay-differential system is not pointwise complete at time t1, then it is also not pointwise complete at time t>t1 and if the linear time-invariant delay-differential system is not pointwise complete at time t=t1 >(n-1)hthen it is also not pointwise complete at time t= >(n-1)h.
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