  In this paper we study time semi-discrete approximations of a class of
exponentially stable infinite dimensional systems with unbounded feedbacks. It
has recently been proved that for time semi-discrete systems, due to high
frequency spurious components, the exponential decay property may be lost as
the time step tends to zero. We prove that adding a suitable numerical
viscosity term in the numerical scheme, one obtains approximations that are
uniformly exponentially stable with respect to the discretization parameter
