Fuzzy systems and controllers: Lyapunov tools for a regionwise approach

This paper reviews a class of tools which can help to check the stability of fuzzy linguistic controllers which is a difficult task due to their regionwise structure. The application of conventional methods when considering a fuzzy controller as a global nonlinear controller often leads to conservative stability results. The use of appropriate continuous or piecewise continuous Lyapunov functions allows to address the stability of nonlinear systems under fuzzy control while taking into account the local structure of the fuzzy controllers. Some methods are presented which enforce the global Lyapunov function to decrease when leaving one subspace for another closer to the equilibrium, using concentric domains and providing less conservative conditions.