We solve the sample-data control problem of output tracking and disturbance
rejection for unstable well-posed linear infinite-dimensional systems. We
obtain a sufficient condition for the existence of finite-dimensional
sampled-data controllers that are solutions of this control problem with
constant disturbance and reference signals. To obtain this result, we study the
problem of output tracking and disturbance rejection in the discrete-time setup
and propose a design method of finite-dimensional controller by using a
solution of a Nevanlinna-Pick interpolation problem with both interior and
boundary conditions. To illustrate our main result, we describe an application
to a delay system of retarded type with output delays.