Thermoacoustic instabilities, frequent in a wide range of combustors, arise from the intricate coupling between the flame’s unsteady heat release and the combustor acoustic. The application of plasma, characterized by its substantial local energy addition and radical generation, has demonstrated potential in disrupting this coupling and thereby mitigating thermoacoustic oscillations. Notably, open-loop control using discharge plasma has been successfully implemented to suppress self-excited oscillations in a Rijke tube setup. Considering the broader context of a complex system that integrates both thermoacoustic systems and discharge plasma, experiments were done to see its performance in stability under different arrangement and discharge repetition rates of discharge plasma. These experimental investigations identified critical operating conditions essential for complete suppression: (A) the optimal location of discharge actuations, and (B) the minimum energy required for complete suppression. Moreover, the impact of discharge plasma, particularly when tuned to the eigenfrequencies of oscillations within the thermoacoustic system, was thoroughly examined. The insights gained from these successful suppression trials are instrumental in guiding the strategic design of both physical arrangement and electrical configurations for the control of combustion instabilities via discharge plasma. Furthermore, through the photographing of the swinging arcs and their thermal disturbances by high-speed camera and high-speed schlieren, the characteristics of arcs’ thermal disturbances and the reasons affecting its suppression effectiveness were determined.