Discrete fuzzy control of time-delay affine takagi-sugeno fuzzy models with H∞ constraint

Takagi-Sugeno (T-S) fuzzy models play an important role in nonlinear control because they can be used to approximate nonlinear systems. Also, for the affine T-S fuzzy models, the local linear sub-system properties can be easily related to the physics of the controlled nonlinear system. This is one advantage of the affine T-S fuzzy models relative to the homogeneous T-S fuzzy models. In the literature, however, most authors have focused on the homogeneous T-S fuzzy models and only a few have considered the affine T-S fuzzy models. Moreover, it is known that time delays exist in physical systems. To date, there has been no study to consider the time-delay effects in the analysis of affine T-S fuzzy models. Therefore the parallel distributed compensation-based H_infin fuzzy control problem for the discrete time-delay affine T-S fuzzy model is now presented. An iterative linear matrix inequality algorithm is used to solve the bilinear matrix inequality problems. Finally, numerical simulation for a time-delayed nonlinear truck-trailer system is given to show an application of the present approach