The paper proposes an optimization-based method for the transient stability assessment of lossy multi-machine power systems. To achieve this objective, a global control Lyapunov function candidate including an auxiliary state is introduced. On this basis, a new excitation control law is proposed. This control law is well-defined provided that an ‘index’ matrix remains non-singular along the closed-loop trajectories. Such a matrix plays a key role in the formulation of an optimization problem, which allows calculating the so-called critical value associated to the introduced Lyapunov function. This permits a direct assessment of transient stability property of the considered post-fault power system. To illustrate the effectiveness of such an optimization-based method, a case study on the model of a three-machine system is presented.