This paper presents a novel scheme for the co-ordinated emergency control of generator-tripping control and Super-conducting Magnetic Energy Storage (SMES). The mathematical foundation of the scheme is based on the proposal of a new Lyapunov function of power systems transient stability analysis derived according to the Hamiltonian systems theory, which is used to quantitatively estimate the necessary control capacity to maintain power system transient stability via the co-ordination of generator-tripping and SMES control in system contingency. Simulation results to test the scheme are presented in the paper.