Takagi-Sugeno fuzzy systems have attracted attentions as proper models for local linearization of nonlinear systems and approximating the behavior of such systems with a kind of interpolation using membership functions. Because of quasi-linear structure, stability analysis and stabilization of these systems have been based on Lyapunov function candidates, which were presented for linear systems, previously. One of the most common Lyapunov functions, for this purpose, is quadratic Lyapunov function which leads to find a common symmetric positive definite matrix between all subsystem matrices. After more than a decade, this method and related algorithms for stabilization based on this function, has proven very fruitful. Also several methods have been proposed to solve some dir=ltr In this thesis we have analyzed stability and proposed a new stabilization approach for continuous time T-S fuzzy systems using a non-derivative Lyapunov function. We have proven that this Lyapunov function implies that the diagonal dominancy of sub-system matrices is a sufficient condition for global asymptotic stability of these fuzzy systems. Also we have used a static feedback controller for stabilization algorithm. If sub-system matrices had uncertain terms in their arrays our approach has the ability to stabilize the system, and places the eigenvalues in a region which leads to a good behavior of states. Also this method can be applied to design fuzzy controllers and use the benefits of such systems.
