Improved Results for T-S Fuzzy Systems With Periodically Varying Delays via a Generalized Delay Derivative-Dependent Reciprocally Convex Matrix Inequality.

In this article, the stability and stabilization for T-S fuzzy systems with periodically varying delays (PVDs) are explored. First, according to the characteristics of PVDs, an augmented Lyapunov-Krasovskii functional (LKF) related to fuzzy rules is established. Second, enhanced stability criteria are developed based on fuzzy augmented LKF together with a generalized delay derivative-dependent reciprocally convex matrix inequality (RCMI). It successfully overcomes the limitations of estimation for only two reciprocally convex terms (RCTs), meanwhile providing a tighter bound by introducing more free variables. Under the parallel distributed compensation (PDC) scheme, a fuzzy memory controller ensuring system stabilization is investigated. Finally, the enhancement of stability criteria and the effectiveness for controller design are verified through numerical simulation.