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When the Takagi–Sugeno (T-S) fuzzy model is used to design controllers for a concerned system, the discrepancy between the system and its T-S fuzzy model becomes crucial sometimes in terms of control performance, particularly in cases when the magnitude of the discrepancy is relatively large. While most existing works have focused on approaches to restrain the influence of the discrepancy, the idea used in this paper is to extract as much information from the discrepancy as possible at first and then use it in the controller design before restraining its influence. By doing so, the magnitude of the discrepancy is reduced accordingly, and thus, better control performance can be expected. Including the discrepancy and other uncertain elements like the inner parameters’ perturbation, a term called uncertainty is considered in this paper. Assuming that the uncertainty influences the system behavior through the state and control input, an observer able to catch the trajectory of the partial uncertainty related to the control input is proposed. Then, a controller employing the trajectory is suggested. All design parameters are obtained by solving certain linear matrix inequalities, which guarantees the system stability. Finally, simulations are provided to illustrate the effectiveness of the proposed approach.

A Controller Design Based on Takagi-Sugeno Fuzzy Model Employing Trajectory of Partial Uncertainty