Control to equilibrium of linear delay-differential systems

A linear time-invariant system with commensurate delays is considered. The system is characterized by two matrices
A(d)
and
B(d)
over
R[d]
(polynominal in the delay operator
d
). It is assumed that the pair (
A, B
) is reachable over the ring
R[d]
. A constructive procedure is derived which, for any initial conditions, finds a solution to system equations such that both the control and the state trajectory become zero identically after some finite time.