  Here we deal with the stabilization problem of non-diagonal systems by
boundary control. In the studied setting, the boundary control input is subject
to a constant delay. We use the spectral decomposition method and split the
system into two components: an unstable and a stable one. To stabilize the
unstable part of the system, we connect, for the first time in the literature,
the famous backstepping control design technique with the direct-proportional
control design. More precisely, we construct a proportional open-loop
stabilizer, then, by means of the Artstein transformation we close the loop. At
the end of the paper, an example is provided in order to illustrate the
acquired results.
