A robustness design of uncertain nonlinear dynamic systems via fuzzy linear control

This study introduces a fuzzy linear control design method for uncertain nonlinear systems with guaranteed control performance. First, the Takagi and Sugeno´s fuzzy linear model is employed to approximate an uncertain nonlinear systems. Next, based on fuzzy linear model, a fuzzy controller is developed to stabilize the fuzzy linear model and at the same time the effect of fuzzy approximation error on control performance is attenuated to a prescribed level. Finally, a robustness performance is achieved in the uncertain nonlinear control system. In the proposed fuzzy linear control method, the fuzzy linear model plays the role of rough control to approximate the nonlinear control system and the H^∞ scheme plays the role of precise control to achieve a robustness performance. Linear matrix inequality (LMI) techniques will be employed to treat this robustness fuzzy control problem. If the state variables are unavailable, a fuzzy observer-based H^∞ control is also proposed to achieve the robustness design of nonlinear uncertain systems