Continuous fuzzy controller design subject to minimizing control input energy with output variance constraints

This paper presents the stability synthesis subject to minimum control input energy and output variance constraints for a class of nonlinear systems, which is modeled by the Takagi-Sugeno (T-S) fuzzy model. For this T-S type fuzzy model, the proposed fuzzy controller design approach not only ensures the stability of the closed-loop system, but also minimizes the control input energy with output variance constraints. The proposed method uses linear matrix inequality technique to find the common positive definite covariance matrix and feedback gains for each rule of the T-S fuzzy models. Finally, the proposed model-based fuzzy control method is used to deal with the control problem of the translational oscillation with a rotational proof mass actuator (TORA) system.