|A generic method for the design of an observer valid for all types of nonlinear systems has not yet been developed. A large class of nonlinear systems can be represented 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.
For a fuzzy model, well-established methods and algorithms exist to analyze the stability or to design fuzzy controllers or observers. Most of these conditions rely on the feasibility of an associated system of linear matrix inequalities that are easy to solve, but are rather conservative.
In this project, we aim to extend existing results and reduce their conservativeness, in particular for distributed and adaptive systems. A possible application is state estimation for traffic networks.