  In this paper we investigate the asymptotic stability of a fourth-order PDE
with a fading memory forcing term and boundary conditions arising from a
flexible robotics model. We carry on our study by using an abstract formulation
of the problem based on the $C_0$-semigroup. To achieve our objective, we first
provide new results on the existence, uniqueness, continuous dependence on
initial data of either mild and strong solutions for semilinear
integro-differential equations in Banach spaces. Then, we also find sufficient
conditions for the uniform asymptotic stability of solutions and for the
existence of attactors. As an application of these abstract results, we can
ensure existence, uniqueness and continuous dependence on initial data for the
solutions of the boundary value problem under investigation and, finally, we
prove the uniform asymptotic stability of solutions and the existence of
attactors under suitable conditions on the nonlinear term.
