Observer-based H ∞ control for Takagi–Sugeno fuzzy systems with uncertainty and disturbance

This article is devoted to the design of a fuzzy-observer-based H_∞ control for an uncertain Takagi–Sugeno fuzzy system with the existence of external disturbance and unavailable state variables. First, an augmented fuzzy model is built by integrating the system state with the output disturbance to create a new variable. Based on Lyapunov theory and linear matrix inequality tools, we derive sufficient conditions for the existence of the fuzzy-observer-based fuzzy controller guaranteeing a generalized H_∞ performance level. A decoupled method is proposed in this study to transform the nonlinear matrix inequality (nonlinear matrix inequality) conditions into some LMI forms. Finally, the procedure of the fuzzy-observer-based H_∞ control design is summarized and the effectiveness is demonstrated with a practical example.