Stabilisation of non-diagonal infinite-dimensional systems with delay boundary control.

Here we deal with the stabilisation 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 stabilise 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 stabiliser, 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. [ABSTRACT FROM AUTHOR]