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This paper proposes a novel Lyapunov-based excitation control (LEC) technique to deal with both global asymptotic stability and voltage regulation for the multi-machine power systems. Lyapunov function is built as a quadratic form of the control objectives consisted of active power offset, rotor speed offset and terminal voltage offset. A completely controllable linear system is constructed to design the trajectories of the time-derivatives of the control objectives. Furthermore, time-derivative of Lyapunov function (TLF) is also expressed as a quadratic form of the control objectives. Feedback gains are chosen to guarantee the negative definition of the TLF for any real number except for the equilibrium point. Therefore, the global asymptotic stability is achieved. The design flexibility of the proposed method provides convenience to introduce the voltage feedback signal for maintaining acceptable voltage level. The system voltage is forced to converge to its reference accompanying with the energy attenuation of Lyapunov function. As a result, voltage deviation is eliminated when Lyapunov function is equal to zero. Finally, a Lyapunov-based decentralized excitation controller is developed for the multi-machine power systems, and it is only related to local measurements. Simulations on a six-machine power system have illustrated better performances in comparison to the existing controllers.