Under the disruption of communication system, the wide area controller may fail to stabilize power oscillations. As a result, the power grids may be jeopardized due to the undamped oscillations. To improve the grid resiliency, a new design method of the two-level robust coordinated stabilizing control of power oscillation damper (POD) of wind turbine with doubly-fed induction generator (DFIG), and power system stabilizer (PSS) is presented in this paper. The two-level control of POD and PSS consists of centralized and local levels. As the main controllers, the centralized POD and PSS are applied to damp out power oscillations. When the communication failure occurs, the local POD and PSS act as the backup controllers to stabilize power oscillations instead of the centralized POD and PSS. The geometric measures of controllability and observability are adopted to determine the suitable input signals of POD and PSS. The structure of POD and PSS is represented by a practical 2^nd-order lead/lag compensator. The control parameters of POD and PSS of each control level are separately optimized under various operating conditions so that the damping effect and robustness can be guaranteed. Simulation study is conducted to show the stabilizing effect of the proposed controller on the enhancement of grid resiliency against severe short circuits, line outages, various power flow levels, wind speeds, variable communication latency, and communication failure.