Design method and application for fuzzy logical controller based on L∞ Lyapunov functions

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_∞ 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_∞ Lyapunov function is the necessary and sufficient stability condition for the time-variant system. A stability criterion based on the L_∞ Lyapunov function is also discussed in the paper. An efficient iterative algorithm is developed to find the L_∞ Lyapunov functions for these control systems