LMI-Based Tracking Control of the Fuzzy Systems: Smooth Compositions Work Better

The paper studies the problem of robust tracking of the fuzzy systems in the presence of uncertainties. A robust feedback controller based on the linear matrix inequality (LMI) is proposed using a Lyapunov function combined with the supervisory controller. Hence, the sufficient stability condition for the general type of robust fuzzy tracking controls has been formulated and the performance of the controller has been tested for different classes of the fuzzy models. It has been demonstrated that the smooth fuzzy compositions have better performance rather than the standard fuzzy compositions, (i.e., min-max compositions and product-sum compositions). Considering that the smooth fuzzy compositions are efficient in face of the uncertainties, it is believed that the present work opens up new doors for wider applications of the smooth fuzzy compositions in the industry.