Lyapunov-like stability theorems for discrete-time fuzzy control systems

Lyapunov-like stability theorems for discrete-time fuzzy control systems are given in this paper. Based on the locality of fuzzy control a set of local Lyapunov functions are used for stability analysis. The stability theorems show that if the fuzzy system can be locally stabilized on every local region, under some boundary conditions the fuzzy system can also be globally stabilized. In this stability approach we apply motions of the system instead of a difference equation of the system. Thus, the method can be used for both model-free and model-based fuzzy controller designs. Finally, an example is given to illustrate the application of the method.