On the state estimation for nonlinear continuous-time fuzzy systems

Abstract

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.

Keywords

• fuzzy systems
• lipschitz analysis
• observer design