This paper addresses the problem of a particular case of high-voltage direct current transmission inserted into a meshed AC grid, which has an inter-area oscillation mode with a higher frequency than the normal mode. The classic Power Oscillation Damping (POD) controller failure to deal with this situation and the other changing operation point cases. Moreover, Non-Minimum Phase Zeros (NMPZs) were systematically put into evidence. Combined with the system uncertainties, they present a serious challange for the control. A same reducedorder model of High-Voltage Direct Current line (HVDC) and adjacent AC area as former research is used for control design in this paper. Based on the reference model, using the LMI optimization method, a Dynamic Output Feedback Controller (DOFC) is proposed to provide modulation of active and reactive power to damp the inter-area oscillations, enhance the damping of the other modes, eliminate some impacts of NMPZs in the system and achieve robustness against variation of the operation point. The linearization and nonlinear models of the system are studied to establish and verify the method. The efficiency and robustness of the proposed controller were tested on the same actual benchmark of 19 generators connected through the mesh AC grid.