Design of <i>H</i> _∞ tracking controller for T-S fuzzy systems

To achieve the tracking control of the Takagi-Sugeno (T-S) fuzzy system, this article proposes an observer-based H ∞ tracking controller design method. First, a fuzzy tracking controller based on state feedback is constructed. Second, to address the unmeasurable problem of system state variables, a fuzzy observer is designed, and the existence conditions of the fuzzy tracking controller and fuzzy observer are derived by using the matrix inequality method. To solve the coupling problem between the design conditions of the fuzzy tracking controller and fuzzy observer, a matrix inequality decoupling strategy is introduced to convert the solving conditions into the standard linear matrix inequality (LMI) form, which realizes the simultaneous solution of the gain matrices of the controller and observer and breaks through the limitations of the traditional two-step method that designs the controller first and then the observer. Finally, the tracking control simulation experiments are carried out on the spring-mass system and single-joint rigid manipulator system. The results show that compared with the traditional two-step method, the proposed method has higher tracking accuracy, and the root mean square error (RMSE) of the system output is significantly reduced.