The paper presents an analytical control solution to the problem of transient stabilization of lossy multi-machine power systems. Firstly, a new form of control Lyapunov function candidates with a flexible potential-energy-like term is proposed. This is achieved mainly by introducing an auxiliary state that contributes to the derivation of a cross-term. Based on the Lyapunov function candidates, a new control law ensuring asymptotic stability of the desired closed-loop operating equilibrium is proposed. Finally, a case study on the model of a two-machine system to illustrate the effectiveness of the proposed control solution is presented.