Nonlinear rule reduction and robust control

We propose an approach for modeling and model reduction using a generalized form of Takagi-Sugeno fuzzy systems. First, we define a generalized form of Takagi-Sugeno fuzzy systems. The structure of these fuzzy systems has some advantages: they accord with dynamics of the original model and they are suitable for reducing the number of rules. Thus, these fuzzy systems are constructed by many if-then rules. Next, we derive the conditions to reduce the number of rules 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 the 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, we illustrate an example of model reduction and robust control for a nonlinear system.