Exponential stability of linear systems under a class of Desch–Schappacher perturbations
Safae El Alaoui,
Mohamed Ouzahra
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.
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