Uncertainty Observer and Controller based on the Takagi-Sugeno Fuzzy Model

A term of uncertainty in the T-S fuzzy model is considered to cover the discrepancy between the concerned system and T-S fuzzy model. Bearing designing a controller based on the T-S fuzzy model in mind, an observer of a partial uncertainty that influences the system through the control matrix the same as the control input is first proposed. The uncertainty observer is capable of estimating either the related uncertainty itself or its trajectory when it is acutely time-varying. Then, a fuzzy controller is designed, in which the estimated uncertainty is used directly to counteract the influence of the uncertainty on the system. In addition, the Nussbaum-type function is also involved in the controller in order to make the closed-loop system asymptotically stable.