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In this paper, a new control synthesis framework is developed to solve a robust stabilization problem for a single-machine infinite-bus power system with a static var compensator (SVC). The uncertainties in the infinite bus voltage and the internal and external reactances to the generating station are considered. First, control inputs for the excitation and the SVC are obtained via immersion and invariance (I&I). Then, the controller is redesigned using a parameter update law and a filter using indirect I&I adaptive control and a two-time-scale technique. The transient and steady-state performances are enhanced by introducing class K functions. The simulation results show that the developed controller improves the system performance. [ABSTRACT FROM AUTHOR]