Contents I. Introduction
There have been several recent studies concerning the stability and the synthesis of controllers and observers for nonlinear systems described by Takagi-Sugeno (T-S) fuzzy models. Based on quadratic Lyapunov function some papers have discussed the feedback control and the state estimation for fuzzy systems [1]–[6], [12]–[14]. For example in [2], stability conditions for fuzzy control systems are reported to relax the conservatism of the basic conditions by considering the interrelations of every two fuzzy subsystems. To less of conservatism other methods to relaxed quadratic stability conditions are also proposed in [6] and [7], collecting the interrelations of fuzzy subsystems into a single matrix, More recently, in [8] new stability conditions are obtained by relaxing the stability conditions of the previous works, which collect the interrelations into a set of matrices. However, in the above paper, the state feedback controllers with parametric uncertainties are not considered. Consequently the robustness of the closed-loop fuzzy model is not guaranteed. In [3], [9]–[10] an approach to design an robust fuzzy control of uncertain fuzzy models was proposed. Unfortunately, the synthesis conditions are very conservative. In [11] another approach was proposed with less conservativeness, which based on [7].
