In recent years, with the growth of wind energy resources, the capability of wind farms to damp low-frequency oscillations (LFOs) has provided a notable advantage for the stability enhancement of the modern power grid. Meanwhile, owing to variations in the power system operating point (OP), the damping characteristics of LFOs may be affected adversely. In this respect, this paper presents a coordinated robust proportional-integral-derivative (PID) based damping control approach for permanent magnet synchronous generators (PMSGs) to effectively stabilize LFOs, while considering power system operational uncertainties in the form of a polytopic model constructed by linearizing the power system under a given set of OPs. The proposed approach works by modulating the DC-link voltage control loop of the grid-side converter (GSC) via a supplementary PID controller, which is synthesized by transforming the design problem into H-infinity static output feedback (SOF) control methodology. The solution of H-infinity SOF control problem involves satisfying linear matrix inequality (LMI) constraints based on the parameter-dependent Lyapunov function to ensure asymptotic stability such that the minimal H-infinity performance objective is simultaneously accomplished for the entire polytope. The coordinated damping controllers for the multiple wind farms are then designed sequentially by using the proposed approach. Eigenvalue analysis confirms the improved damping characteristics of the closed-loop system for several representative OPs. Afterward, the simulation results, including the performance comparison with existing approaches, validate the higher robustness of the proposed approach for a wide range of operating scenarios.