Synthesis of Discrete Nonlinear Passive Systems via Affine T-S Fuzzy Models with Input Energy Constraints

In this paper, a Takagi-Sugeno (T-S) fuzzy controller is designed to deal with input energy constrained control problem for the discrete-time nonlinear passive systems which are presented by affine T-S fuzzy models. The stability conditions developed by Lyapunov theory are characterized as a bilinear matrix inequality (BMI) problem for the synthesis of the discrete-time nonlinear passive affine T-S fuzzy systems. It can not be solved via an 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 present approach.