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This paper presents a study on a robust H2 LMI-based damping control scheme, for improving the inter-area mode oscillations of power systems. A reduced order centralised controller is designed for a 16-machine, 5-area power system (138th order) model reinforced with a thyristor controlled series capacitor (TCSC) to improve the damping of the critical inter-area modes by employing appropriate signal measurements. The effectiveness of the linear matrix inequalities (LMl) formulation, using pole location constraints, of the problem is illustrated. Robustness to faults and unknown disturbances is guaranteed via the design procedure. The performance of the designed system is assessed itt the frequency domain and via appropriate time-domain simulations based upon the non-linear model under various scenario.