Exponential stability of linear systems under a class of Desch–Schappacher perturbations

Abstract

In this paper, we investigate the uniform exponential stability of the system where the unbounded operator is the infinitesimal generator of a linear semigroup of contractions in a Hilbert space and is a Desch–Schappacher operator. Then we give sufficient conditions for exponential stability of the above system. The obtained stability result is then applied to prove the uniform exponential stabilization of some bilinear partial differential equations.