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Power system low frequency oscillations influence dynamic behaviour of a complex power system and threaten its security. The dynamic performance of power system can be improved by damping low frequency oscillation with the help of supplementary controllers. This paper presents the design of supplementary controller for Static Var Compensator (SVC) to damp low frequency, in particular inter-area oscillations. The controller is designed based on H∞ loop-shaping technique in which the robust stabilization of the normalised coprime factor plant is formulated into a generalized H∞ problem. Moreover, the selection of proper feedback signal from the available measurements of the system plays vital role in designing the controller. The residue analysis is used to select the suitable locally available signal as an input signal to the proposed controller. Two power systems with varying sizes and complexities are used to test with the design of the proposed controller. The power systems include the benchmark, two-area system for low frequency oscillation studies and a modified version of a practical system. Both eigenvalue analysis and time domain simulations are used to study the performance of the proposed H∞ controller.