The extended equal-area criterion（EEAC） maps multi-machine system trajectories into a series of time-varying one-machine infinite-bus（TV-OMIB） system trajectories through complementary-clusters center-of-inertia relative-motion（CCCOI-RM） transform. The information of oscillation modes is strictly decoupled. The dominant oscillation mode is identified to implement quantitative analysis for stability. The concepts on trajectory eigenvalue are introduced to reflect the affects of nonlinearity on oscillation characteristics. The sensitivity of trajectory eigenvalue to generator damping is proposed to reflect participating factor of individual generators. It is discovered that adjusting generator power based on the reducing tie-line power criterion may induce negative damping effect. The criterion of adjusting generator based on reducing image power angle will damp low-frequency oscillation. The effect of disturbance under different intension to system oscillation is analyzed. Simulations show that system oscillation characteristic around bifurcation point may be different from the eigenvalue of equilibrium point.