Based on the theory of Lyapunov and due to the characteristics of inter-area oscillation mode： low-frequency,low damping and long duration,the theory of Gutman is used to extend the stability region for redefining a non-convex stable region to quickly promote the system to stable state. The eigenvalue shift factor is applied to convert the nonlinear non-convex region into a feasible linear space. With the consideration of the uncertainties of system and disturbance,the constraints of hybrid H2 ／ H∞ multi-objective robust control are reformed based on the non-convex stable region and transformed into a series of linear inequality set,which are optimized to obtain the feedback control vectors. Time-domain and frequency-domain simulations are respectively carried out for a 4-machine 2-area system under different operating conditions,and results show that,the proposed control strategy is superior to traditional H2 ／ H∞ control strategy in damping performance and robustness.