Although the fuzzy logic controller(FLC) has been adopted in many engineering applications, its performance is not guaranteed since there is no definite theoretic analysis. It may be the main factor that one hesitates to adopt the FLC in critical applications. In this paper, observing the similarity in the pattern of control input between the FLC and a conventional robust controller, i.e., the variable structure controller, we present theoretic analysis for robustness of a fuzzy control system based on the Lyapunov theory.