Robust Fuzzy Observer-Based Fuzzy Control Design for Nonlinear Discrete-Time Systems With Persistent Bounded Disturbances

To date, nonlinear l _infin- gain control problems have not been solved by the conventional control methods for nonlinear discrete-time systems with persistent bounded disturbances. This study introduces fuzzy observer-based fuzzy control design, where the premise variables depend on the state variables estimated by a fuzzy observer, to deal with the nonlinear l _infin-gain control problem. The fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables depend on the state variables. First, the Takagi-Sugeno (T-S) fuzzy model is employed to represent the nonlinear discrete-time system. Next, based on the fuzzy model, a fuzzy observer-based fuzzy controller is developed to minimize the upper bound of l _infin-gain of the closed-loop system under some nonlinear matrix inequality (non-LMI) constraints. A novel decoupled method is proposed in this study to transform the non-LMI conditions into some linear matrix inequality (LMI) forms. By the proposed decoupled method and the genetic algorithm, the l _infin-gain fuzzy observer-based fuzzy control problem for the nonlinear discrete-time systems can be easily solved by an LMI-based optimization method. The proposed methods, which efficiently attenuate the peak of perturbation due to persistent bounded disturbances, extend the l _infin-gain control problems from linear discrete-time systems to nonlinear discrete-time systems. A simulation example is given to illustrate the design procedures and to confirm the l _infin-gain performance of the proposed method.