Lmi-based Fault Detection Fuzzy Observer Design with Multiple Performance Constraints for a Class of Non-linear Systems: Comparative Study

In view of the conservatism of the conventional linear matrix inequality (LMI) based fault detection observer design for Takagi-Sugeno fuzzy nonlinear systems with more If-Then rules, an improved fuzzy observer design is presented. The identical transformation of matrix inequalities is employed to reduce the conservatism and the number of LMI constraints, which can accommodate to the models with more rules. The multiobjective optimization strategy is also applied to dealing with the multiobjective constraints on the disc poles index, the quasi L2-norm indices of the residual’s robustness to disturbances and sensitivity to faults. The resulting observer not only is less conservative, but also meets the multiple performance requirements of fault detection. Meanwhile, two other methods are introduced for comparative study. Moreover, to enhance the effect of fault detection in residual evaluation, a weighted BIC criterion-based algorithm is introduced to determine the finite-time window for online evaluation. Simulative examples demonstrate the effectiveness of the proposed method.