On the state estimation for nonlinear continuous-time fuzzy systems

A large class of nonlinear systems can be represented or well approximated by Takagi-Sugeno (TS) fuzzy models, which in theory can approximate a general nonlinear system to an arbitrary degree of accuracy. The TS fuzzy model consists of a fuzzy rule base. The rule antecedents partition a given subspace of the model variables into fuzzy regions, while the consequent of each rule is usually a linear or affine model, valid locally in the corresponding region. In this paper, the observer design problem for a T-S fuzzy system subject to Lypschitz perturbation is investigated. First, an observer of Kalman type is designed to estimate the unknown system states. Then, the class of one-sided Lipschitz for a TS fuzzy system subject to a sufficient condition on the bound is studied. The challenges are discussed and some analysis oriented tools are provided. An example is given to show the applicability of the main result.