  Suppose that a continuous-time linear infinite-dimensional system with a
static state-feedback controller is strongly stable. We address the following
question: If we convert the continuous-time controller to a sampled-data
controller by applying an idealized sampler and a zero-order hold, will the
resulting sampled-data system be strongly stable for all sufficiently small
sampling periods? In this paper, we restrict our attention to the situation
where the generator of the open-loop system is a Riesz-spectral operator and
its point spectrum has a limit point at the origin. We present conditions under
which the answer to the above question is affirmative. In the robustness
analysis, we show that the sufficient condition for strong stability obtained
in the Arendt-Batty-Lyubich-V\~u theorem is preserved between the original
continuous-time system and the sampled-data system under fast sampling.
