A Reduction in Conservatism in Stability and L2 Gain Analysis of Takagi-sugeno Fuzzy Systems via Linear Matrix Inequalities

In this paper, we use a state-dependent Lyapunov function to reduce the conservatism in stability analysis of Takagi-Sugeno (T-S) fuzzy systems via Linear Matrix Inequalities (LMIs). Our approach uses T-S fuzzy rules to deene Lyapunov functions, and therefore substantially enlarges the class of Lyapunov functions which can be used to prove stability of T-S fuzzy systems. This approach greatly reduces the conservatism and generalizes previous results in this area which relied on nding a common positive deenite Lyapunov function. Since the resulting Lyapunov function is state-dependent, this method requires a priori bounds on the variations of those states that are the argument of the membership functions. The eeectiveness of this approach is nally presented via a simple numerical example.