Fuzzy observer-based fuzzy control design for nonlinear systems with persistent bounded disturbances

To date, nonlinear L∞-gain control problems have not been solved by the conventional control methods for the nonlinear dynamic systems with persistent bounded disturbances. This study introduces a fuzzy control design to deal with the nonlinear L∞-gain output feedback control problem. First, the Takagi and Sugeno (T–S) fuzzy model is employed to approximate the nonlinear dynamic system. Next, based on the fuzzy model, a fuzzy observer-based fuzzy controller is developed to minimize the upper bound of L∞-gain of the closed-loop system under some linear matrix inequality (LMI) constraints. Therefore, the nonlinear L∞-gain control problem is transformed into a suboptimal control problem, i.e., to minimize the upper bound of the L∞-gain of the closed-loop system subject to some LMI constraints. In this situation, the nonlinear L∞-gain output feedback control problem can be easily solved by a LMI-based optimization method. The proposed methods, which efficiently attenuate the peak of perturbation due to persistent bounded disturbances, extend the L∞-gain control problems from linear dynamic systems to nonlinear dynamic systems.