Discrete fuzzy control of time-delay affine Takagi–Sugeno fuzzy models with H1 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 H1 fuzzy control problem for the discrete timedelay 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.