Linearization of T-S fuzzy systems and robust H ∞ control

Takagi-Sugeno (T-S) fuzzy model is difficult to be linearized because of membership functions included. So, novel T-S fuzzy state transformation and T-S fuzzy feedback are proposed for the linearization of T-S fuzzy system. The novel T-S fuzzy state transformation is the fuzzy combination of local linear transformation which transforms local linear models in the T-S fuzzy model into the local linear controllable canonical models. The fuzzy combination of local linear controllable canonical model gives controllable canonical T-S fuzzy model and then nonlinear feedback is obtained easily. After the linearization of T-S fuzzy model, a robust H ∞ controller with the robustness of sliding model control (SMC) is designed. As a result, controlled T-S fuzzy system shows the performance of H ∞ control and the robustness of SMC.