H∞ fuzzy control for discrete affine Takagi-Sugeno fuzzy models with time delay effect

The affine Takagi-Sugeno (T-S) fuzzy model played a more important role in nonlinear control because it can be one of the useful control approaches for complex nonlinear systems. Besides, it is known that the time delays exist in physical systems and the previous works didn't consider the time delay effects in the stability analysis of affine T-S fuzzy models. Hence, this paper deals with the Parallel Distributed Compensation (PDC) based H-infinity fuzzy control problem for the discrete time-delay affine T-S fuzzy models. The synthesis for the discrete time-delay affine T-S fuzzy models is a Bilinear Matrix Inequality (BMI) problem and it can not be solved via a convex optimization algorithm. Thus, an Iterative Linear Matrix Inequality (ILMI) algorithm is used to solve this BMI problem in this paper. Finally, a numerical simulation is given to show the applications of the proposed design approach.