This paper presents a new control scheme for the design of damping controllers for power systems. The scheme is based on the combination of two powerful control techniques, namely the Linear Matrix Inequalities (LMI) techniques and the Direct Feedback Linearization (DFL). It is shown that the DFL can cancel nonlinearities in the power system model, thus reducing the uncertainty in the LMI design. The obtained results show the proposed controller provides smooth control actions and fast transient response, being well-suited for the low frequency oscillations problem.