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In this work, we propose wide-area measurement based control mechanism for future smart transmission grid applications. The design comprises measurements obtained from local area and geographically isolated remote area to damp out local and inter-area low-frequency oscillation mode to ensure desired dynamic performance of the large scale interconnected power transmission grid system. The synchronized measurement obtained from PMU sensors are used as an input to the proposed design. Lyapunov-like energy functional is used to derive stability property of the closed loop electric power transmission system. Delay independent asymptotic convergence conditions are derived by using linear matrix inequality (LMI) condition. Finally, simulation on a single machine connected to large electric power transmission grid networks to illustrate the effectiveness of the theoretical development of this paper.