This work centers on robust compensating function scheme for adequate electrical power system stabilization. There has been high level of disturbances in the power line and lack of adequate compensation technique to cancel the effects of the resultant instability which has caused power failures. The problem was addressed by the consideration of disturbances in the power line during the design of the compensating function for the improvement of the power system performance and stability. H-Infinity synthesis robust compensating function design method was used to design an adequate compensator that can improve the performance and stability of the power system.  From the results, the H-infinity Synthesis Controlled Generating Plant (HCGP) recorded an overshoot of 0%, settling time of 1.04 seconds, tracking error of 0dB, gain margin of 21.7dB and phase margin of 79.6 degrees. The simulation was repeated by varying the value to k to -0.3, and the generating plant produced same results. This shows that the system can maintain performance and stability equilibrium even when there is change in its parameters. Since the HCGP satisfied the performance and stability robustness, therefore it was concluded that power system robust compensating function scheme for improved performance and stability robustness was achieved using H-Infinity synthesis method.