  This paper studies the boundary feedback stabilization of a class of diagonal
infinite-dimensional boundary control systems. In the studied setting, the
boundary control input is subject to a constant delay while the open loop
system might exhibit a finite number of unstable modes. The proposed control
design strategy consists in two main steps. First, a finite-dimensional
subsystem is obtained by truncation of the original Infinite-Dimensional System
(IDS) via modal decomposition. It includes the unstable components of the
infinite-dimensional system and allows the design of a finite-dimensional delay
controller by means of the Artstein transformation and the pole-shifting
theorem. Second, it is shown via the selection of an adequate Lyapunov function
that 1) the finite-dimensional delay controller successfully stabilizes the
original infinite-dimensional system; 2) the closed-loop system is
exponentially Input-to-State Stable (ISS) with respect to distributed
disturbances. Finally, the obtained ISS property is used to derive a small gain
condition ensuring the stability of an IDS-ODE interconnection.
