Improvement on the problem of optimal fuzzy H∞-tracking control design for non-linear systems

This study is concerned with the problem of output feedback fuzzy H_∞-tracking control design for non-linear systems. The non-linear system is represented by using the Takagi and Sugeno fuzzy modelling scheme. The final controller takes the form of parallel distributed compensation. The final controller results in the stability of the closed-loop system and the H_∞ tracking of a bounded reference signal. Existing approaches to this problem available in the literature implement an observer-based output feedback controller. These approaches lead to a non-linear matrix inequality condition, which can be partially solved by applying a double-step algorithm. The approach presented in this study is based on a new structure for the controller. In this approach, the problem formulation and the method of finding the controller parameters involve a single-step linear matrix inequality form. Moreover, it is possible to easily find the optimal controller from the whole solution set. The approach is also extended to the case of non-linear time-delay systems. Finally, two examples are given to illustrate the effectiveness of the obtained results in comparison with the existing methods.