A stability analysis and controller design for fuzzy logical systems described by the Takagi-Sugeno model is introduced, and this method is based on a common L-infinity Lyapunov function method. The fuzzy logical controller with a parallel distributed compensation structure is employed, and then the overall closed-loop system can be represented by a time-variant system. It is proved that the existence of the L-infinity Lyapunov function is the necessary and sufficient stability condition for the time-variant system. A stability criterion based on the L-infinity Lyapunov function is also discussed in the paper. An efficient iterative algorithm is developed to find the L-infinity Lyapunov functions for these control systems.