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Electric power system is complex interconnected system that is subjected to rapid change in its structure. Addition of new equipment, operation close to stability limits and variation in load in summer and winter are some factors that make power system unstable and introduce electro-mechanical oscillations in the system. Electro-mechanical oscillations of small magnitude often persist for long periods of time and restrict the power transfer capacity. These oscillations can further increase with the variation in load and system operating points. To stabilize the power system different control strategies are used to damp the oscillations. In the past, the dynamic stability of power system was modeled using linearized modeling of power system at operating points. Linear eigenvalue controllers damp the oscillation to some extent but are not robust for disturbance and variation in system operating points and therefore can render system unstable. Non-linear controller design has found extensive application in robotics for stabilizing system. Synergetic Controller based on Synergetic Control Theory, is a non-linear controller that forces the system towards global stability and has extensively been used in power electronics. In this research, a Single Machine Infinite Bus (SMIB) with HVDC link is considered for comparing the performance of linear and non-linear controllers. The test system has Static Var Compensator (SVC) connected on load bus. Reactive modulation is performed through SVC to damp oscillations in the system. The Synergetic Controller is designed for full transient model and the classical model of the synchronous machine. The performance of both non-linear controller and linear controller is compared for different disturbance and variation in system parameters. Results show the robustness of non-linear controller which damps the oscillations effectively. I would like to especially thank my adviser Dr. Muhammad Akram Choudhry for his guidance, support and encouragement throughout this research and my Master's program. He has impacted into my life an immense deal of knowledge and without him, this work would not have been accomplished. I am very grateful to Dr. Ali Feliachi for his advice, support and guidance. I would like to also thank Dr. Vinod Kulathumani for his time and guidance. Also, I appreciate all the faculty members who have taught, encouraged and guided me in special and different ways. Special thanks goes to my parents and my family members. Due to their immense support I am able to complete this work.