Exponential stability of the plate equations with potential of second order and indefinite damping

We study the exponential stability of the plate equations with potential of second order and indefinite sign damping term. By means of a global Carleman-type estimate and the usual perturbation method, we show that the energy of the system decays exponentially provided that the negative damping is sufficiently small. Both the energy decay rate and the upper bound estimate on the negative damping are given explicitly.