Modeling and model reduction using generalized form of Takagi-Sugeno fuzzy systems

We propose modeling and model reduction using 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. One is that this fuzzy systems accord with dynamics of the original model. The other is that it is 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 which 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, we illustrate an example of model reduction and robust control for a nonlinear system