L∞ - gain fuzzy control for nonlinear dynamic systems with persistent bounded disturbances

To date, nonlinear L_∞ - gain control problems have not been solved by the conventional control methods for nonlinear dynamic systems with persistent bounded disturbances. This study introduces a fuzzy control design to deal with the nonlinear L_∞ - gain 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, the upper bound of L_∞ - gain of the closed-loop system can be obtained under some linear matrix inequality 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 control problem can be easily solved by LMI-based optimization method. The proposed methods, which efficiently attenuate the peak of error signal due to persistent bounded external disturbances, extend the L_∞ - gain control problems from linear dynamic systems to nonlinear dynamic systems.