Fuzzy controller design for singular affine T-S fuzzy models

This paper presents a fuzzy controller design method for the singular nonlinear systems with perturbations via singular affine Takagi-Sugeno (T-S) fuzzy models. The Parallel Distributed Compensation (PDC) technique is applied to design this fuzzy controller for the singular affine T-S fuzzy model. However, the derived stability conditions with the fuzzy controller are Bilinear Matrix Inequality (BMI) problems which cannot be calculated by the optimal convex programming algorithm of Linear Matrix Inequality (LMI) method directly. In order to solve the present design problem, the BMI problems must be transferred into the LMI problems. Hence, an Iterative Linear Matrix Inequality (ILMI) algorithm is developed to find the feasible solutions for the stability conditions. Finally, a numerical example is provided to demonstrate the applications and effectiveness of the proposed fuzzy control approach.