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

Abstract

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