Fuzzy-Model-Based Sampled-Data Control of Chaotic Systems: A Fuzzy Time-Dependent Lyapunov–Krasovskii Functional Approach

This paper addresses the sampled-data stabilization problem for chaotic systems represented by Takagi–Sugeno (T–S) fuzzy models. If the upper bounds for the time derivative of membership functions are available, combining the fuzzy blending for some quadratic functions together with the introduction of some new useful terms, a novel fuzzy time-dependent Lyapunov–Krasovskii functional (LKF) is proposed to fully capture the available characteristics of the actual sampling pattern and membership functions simultaneously. Based on the proposed LKF, a new criterion dependent on the upper bounds for the time derivative of membership functions is presented to guarantee the asymptotic stability of the whole closed-loop system. Moreover, a stability criterion independent of the upper bounds is also provided based on the corresponding common time-dependent LKF. Then, the designed fuzzy sampled-data controller can be synthesized by analyzing the corresponding stabilization conditions. Moreover, a search algorithm is provided to find the optimal tuning parameters. Finally, one practical example of the Lorenz system is given to illustrate that much less conservativeness can be achieved compared with the earlier results by using the corresponding common LKF, and the results can be further improved when adopting the fuzzy time-dependent LKF within large upper bounds.