H∞ Model Reduction for Takagi–Sugeno Fuzzy Systems via Space Projection

In this paper, the problem of model reduction for Takagi-Sugeno (T–S) fuzzy systems is studied. The virtual inner disturbance is first constructed to map a potential link between the states of two systems before and after dimensionality reduction. Based on Lyapunov theorem, the H∞ approach is then used to analyze the augmented system with the inner disturbance. The results are unrelated to reduced-order system membership functions (MFs), which can be freely selected. Furthermore, both the number of rules and the size of the reduced-order system and the inner disturbance may be flexibly chosen. An example is adapted to demonstrate the efficiency of the proposed method.