Stability Bounds for Fuzzy Estimation and Control

A large class of nonlinear systems can be well approximated by Takagi-Sugeno fuzzy models, for which methods and algorithms have been developed to analyze their stability and to design observers and controllers. However, results obtained for Takagi-Sugeno fuzzy models are in general not directly applicable to the original nonlinear system. In this paper, we investigate what conclusions can be drawn and what guarantees can be expected when an observer or a state feedback controller is designed based on an approximate fuzzy model and applied to the original nonlinear system. We also investigate the case when an observer-based controller is designed for an approximate model and then applied to the original nonlinear system. In particular, we consider that the scheduling vector used in the membership functions of the observer depends on the states that have to be estimated. The results are illustrated using simulation examples.