Function space null controllability by augmented delay feedback control

The linear finite-dimensional system
\dot{x}(t)=Ax(t) + u(t)
cannot, by linear delay feedback controls of the form
u(t)= \sum \min{i = 1}\max{m}[B_{i}x(tih) + C_{i}\dot{x}(t-ih)]
, be controlled such that
x(t) \equiv 0
for
t
large enough. A simple and presumably practical way is proposed of circumventing this limitation of standard delay feedback design. This method consists in augmenting the original system by a linear system of the same dimension and using linear feedback from the augmented system. Parameters in the delay feedback control laws are determined which yield function space null controllability in minimal time.