Stability of infinite-dimensional sampled-data systems with unbounded control operators and perturbations

We analyze the robustness of exponential stability infinite-dimensional sampled-data systems with unbounded control operators. The perturbations we consider are so-called Desch–Schappacher perturbations, which arise, e.g., from boundary described by partial differential equations. As main result, show that system is preserved under all sufficiently small in a certain sense.