A Lyapunov Analysis for Mamdani Type Fuzzy-Based Sliding Mode Control

We derive sufficient conditions to guarantee asymptotic stability for fuzzy-based sliding mode controllers applied to single-input single-output nonlinear systems, made in the framework of the Lyapunov functions. Such conditions also preserve the well-recognized features of both sliding mode control and Mamdani-type fuzzy control such as robustness and uncertainties treatment. In addition, the rules for tuning the cores of membership functions are also found. Real-time experiments, made on a one-link pendulum, are performed to illustrate and demonstrate the theoretical results.