Estimation of the asympototic stability region of uncertain fuzzy systems with bounded controllers using variable structure system design approach

In this paper, the problem of estimating the asymptotic stability region (ASR) of uncertain nonlinear systems is considered. Our approach is based on Takagi-Sugeno (T-S) fuzzy model and variable structure control (VSC) technique. To simplify the problem, we use a state transformation to reduce the system order of the T-S fuzzy systems. Then we design the sliding surface for the transformed system. By the Lyaponov stability theorem, the ASR can be estimated. A simulation example is presented to verify the effectiveness of the proposed scheme.