Robust fuzzy observer-based fuzzy control design for nonlinear systems with persistent bounded disturbances: A novel decoupled approach

Unlike the L 2 -gain ( H ∞ ) control case, the L ∞ -gain control problem is dealing with persistent bounded disturbances. This study introduces L ∞ -gain fuzzy observer-based fuzzy control design, where the premise variables depend on the state variables estimated by a fuzzy observer, for nonlinear systems via T–S fuzzy models. The fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables do not depend on the state variables estimated by a fuzzy observer. A novel decoupled method is proposed in this study to transform the non-LMI conditions into some LMI forms. By the proposed decoupled method and the genetic algorithm, the L ∞ -gain fuzzy observer-based fuzzy control problem can be easily solved by an LMI-based method.