Stability and Stabilization for Delayed T–S Fuzzy Systems via the Membership-Dependent Free-Weighting-Matrices Method

This article studies the stability and stabilization of delayed Takagi–Sugeno fuzzy systems (TSFSs). First, by introducing the membership functions into the free matrices, a membership-dependent (MD) Free-weighting-matrices (FWMs) method containing the variable-augmented-based FWMs method is proposed. This method can avoid the time-varying delay-dependent higher-order terms in the derivatives of the Lyapunov-Krasovskii functionals and introduce MD information. Then, an improved stability criterion is derived by applying the MD FWMs approach with the generalized free-matrix-based inequality. Moreover, through the parallel distributed compensation technology, a related controller design approach for the closed loop TSFS is developed. Finally, four known numerical examples are shown to validate the improvements and advancements of the presented method.