In this paper, for the situation of HVDC inserted in meshed AC power grid, a Model-matching robust H ∞ static output error feedback controller (RSOFC) and model-matching dynamic decoupled output feedback controller (DDOFC) are proposed to improve the damping of inter-area oscillation modes and maintain robustness to face the effects of different operating points and unstable zeros. Sufficient conditions for robust stability are derived in the sense of Lyapunov asymptotic stability and presented in the form of linear matrix inequalities to obtain H ∞ RSOFC and DDOFC gains based on the reference model. The efficiency and robustness of the proposed controllers are tested and compared to Linear-Quadratic-Gaussian (LQG) control, mixed sensitivity H ∞ , standard (IEEE) Power Oscillation Damping (POD) controllers on a realistic benchmark of 19 generators connected by a meshed AC grid. The main contributions of this paper are: (i) Compensate the negative effect of unstable zeros (non-minimum phase behavior) on the performances of the closed-loop; (ii) the robustness is improved in order to provide good responses in case of network variations (load evolution, line, and generator trips, etc.) and HVDC line parameters changes; (iii) improve the damping compared with standard controller structures (LQG, mixed sensitivity H ∞ and standard POD controller).