Robustness design of nonlinear dynamic systems via fuzzy linear control

This study introduces a fuzzy linear control design method for nonlinear systems with optimal H1 robustness performance. First, the Takagi and Sugeno fuzzy linear model is employed to approximate a nonlinear system. Next, based on the fuzzy linear model, a fuzzy controller is developed to stabilize the nonlinear system, and at the same time the effect of external disturbance on control performance is attenuated to a minimum level. Thus based on the fuzzy linear model, H1 performance design can be achieved in nonlinear control systems. In the proposed fuzzy linear control method, the fuzzy linear model provides rough control to approximate the nonlinear control system, while the H1 scheme provides precise control to achieve the optimal robustness performance. Linear matrix inequality (LMI) techniques are employed to solve this robust fuzzy control problem. In the case that state variables are unavailable, a fuzzy observer-based H1 control is also proposed to achieve a robust optimization design for nonlinear systems. A simulation example is given to illustrate the performance of the proposed design method.