Boundary stabilization for a hybrid system of viscoelasticity

In this paper, we study the boundary feedback stabilization of a hybrid system that is composed of a viscoelastic thin plate with one part of its edge clamped and the remaining free part attached to a viscoelastic rigid body. By adopting the frequency domain method, we prove that the boundary feedback controls together with the dissipation induced by the memory effect are strong enough to secure the result of the exponential stability of energy. We also reach the result of the exponential stability of the hybrid system on the domain with corners without any extra hypotheses on the regularity of solutions.