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The paper presents the design of function based variable structure fuzzy controllers for flexible AC transmission systems to improve transient stability performance. This controller is tested on a very widely considered FACTS device like static compensator (STATCOM) which is simulated by a current injection model comprising both real and reactive components. The function based fuzzy controller uses the Takagi-Sugeno scheme and generates the proportional action which by one-to-one or one-to-two mapping can produce the variable gain PI controller. Unlike the performance based two input fuzzy controllers considered earlier, the function based one input fuzzy controller dispenses with gain dependency and provides independent tuning for proportional and integral gains. This new fuzzy controller is tested on a single-machine infinite-bus power system operating with a STATCOM for a variety of transient disturbances and variation of operating point to validate its superior performance in comparison to the conventional PI controllers.