Lyapunov function based design of robust fuzzy controllers for uncertain nonlinear systems: distinct Lyapunov functions

This paper presents the stability and robustness analyses of an uncertain fuzzy control system which is formed by an uncertain fuzzy plant model and a fuzzy controller. The fuzzy plant model with parameter uncertainties describes exactly the behavior of an uncertain nonlinear plant. Three design approaches are introduced to close the feedback loop. Based on the Lyapunov's stability theory, new stability criteria and robust areas are derived without resorting to a common Lyapunov function. An application example on stabilizing an uncertain nonlinear mass-spring-damper system is given to illustrate the merit.