This paper presents the pseudo-generalized Hamiltonian theory which has a more general form and a wider range of application. A new Lyapunov candidate function is proposed and proven to qualify as a true Lyapunov function under some assumptions. Then, we take multi-machine power system considering transfer conductance as an example to illustrate the application of the theory proposed in this paper. A global centralized excitation control strategy is designed by L 2 -disturbance attenuation method. Simulation results demonstrate the effectiveness of the proposed methodology.