Sampled-Data Control Design for T-S Fuzzy System via Quadratic Function Negative-Determination Approach

This study investigates the stability characteristics of the Takagi-Sugeno (T-S) fuzzy system under the sampled-data control (SDC). The considered SDC-based T-S fuzzy system is represented as a T-S fuzzy system with varying time delays, which is based on the input delay method. Next, a proper Lyapunov-Krasovskii functional candidate is formulated along with a quadratic delay product term. By employing the generalized reciprocally convex combination lemma, some sufficient conditions are established in terms of linear matrix inequality (LMI), which ensures the stability of the considered T-S fuzzy system under the designed SDC. This LMI condition can be checked by means of a relaxed negative-determination lemma of quadratic polynomials and has less conservatism. Finally, the usefulness and the superiority of the designed approach will be validated by means of numerical examples.