Inter-area oscillations are associated with machines in one part of the system oscillating against machines in other parts of the system. They are caused by two or more groups of machines that are interconnected by weak ties. To damp out the inter-area oscillations, this paper proposes the new application of wide area stability control for robust centralized power oscillation dampers (PODs) design of doubly-fed induction generator (DFIG) wind turbines. The POD with 2^nd-order lead/lag compensator structure for each DFIG wind turbine is located at the control center. To stabilize the target inter-area mode effectively, the geometric measures of controllability and observability are used to choose the suitable DFIG wind turbine for stabilizing the target oscillation mode, the proper input signal of POD, and the location of phasor measurement units (PMUs). The input signal of each POD is obtained from PMU while the output signal is transmitted to the rotor side converter voltage controller of DFIG. As a result, the reactive power output of DFIG can be modulated to damp out inter-area oscillations. In the POD parameters optimization, the wide range of power output levels of DFIGs and synchronous generators, time delays due to wide area communication, and unstructured system uncertainties model are taken into account so that the damping of inter-area modes and the system robust stability margin against uncertainties can be guaranteed. Solving the problem by the firefly algorithm automatically, the optimal parameters of PODs can be achieved. The stabilizing performance and robustness of the proposed robust centralized POD are evaluated in the IEEE New England 39 bus system by eigenvalue analyses and nonlinear simulation in scenarios with severe short circuits, N-1 outage contingencies, heavy power flows, and line tripping.