Generalized Takagi-Sugeno fuzzy systems: Rule reduction and robust control

This paper presents model reduction and robust control using a generalized form of Takagi-Sugeno fuzzy systems. We first define a generalized form of Takagi-Sugeno fuzzy systems. The generalized form has a decomposed structure for each element of Ai and Bi matrices in consequent parts. The key feature of this structure is that it is suitable For reducing the number of rules. Conditions to reduce the number of rules are represented in terms of LMIs. The main idea is to find a structure of if-then rules of the reduced model that agrees well with dynamics of the original model. Furthermore, we estimate the lower bound of the norm of model uncertainty of the Takagi-Sugeno fuzzy system that can cover the reduction error. Finally, an example of model reduction and robust control for a nonlinear system is illustrated. In this example, we achieve a robust controller design so as to compensate the uncertainly of the Takagi-Sugeno fuzzy system.