Stability and Stabilization of T-S Fuzzy Systems With Sampled-Data Controller: A Fuzzy-Related Matrix Injection Method

This article addresses the stability and stabilization issues of Takagi–Sugeno (T-S) fuzzy systems under sampled-data control. In this article, efforts are dedicated to developing a stability criterion and control strategy with high accuracy and low complexity, leveraging an improved looped functional and a fuzzy-related matrix injection method. First, an improved looped function containing quadratic information about the sampling sawtooth characteristic is employed to include as much system state information as possible in a simple form. In response to the nonlinear terms encountered in the functional derivatives, a fuzzy-related matrix injection method is proposed on the basis of linearization transformation. This method enables the unified treatment of reciprocally convex and quadratic terms, which is conducive to reducing estimation gaps. Based on the aforementioned techniques, stability and stabilization criteria for T-S fuzzy systems are derived. The efficacy and superiority of the proposed method are substantiated through rigorous theoretical analysis and illustrative instances.