ABSTRACT
Stability is one of the most important and fundamental issues for control systems. One critical problem with conventional fuzzy logic control systems is the difficulty encountered in stability analysis of such systems and in systematic design of control laws. It is believed the problem arises from the model-free concept of conventional fuzzy control systems although this concept is very useful in many control engineering applications, especially when models of the systems to be controlled are not available. With the introduction of T-S fuzzy models, stability analysis of fuzzy control systems becomes much easier, and more important, it can be handled in the same way as conventional model based control systems. In particular, stability analysis of T-S fuzzy systems has been pursued mainly based on Lyapunov stability theory with a variety of Lyapunov functions. Three of the most popular are the so-called common (or global) quadratic, piecewise quadratic, and fuzzy (or nonquadratic) Lyapunov functions. This chapter is devoted to stability analysis of T-S fuzzy systems based on these Lyapunov functions.
