Filtering for polynomial fuzzy systems using polynomial approximated membership functions

This paper investigates the filtering problem of polynomial fuzzy-model-based (PFMB) nonlinear systems. A novel polynomial fuzzy filter is designed to guarantee that the filter error system is asymptotically stable and satisfies a desired performance. Polynomial approximated membership functions obtained by Taylor series are employed for filtering analysis. Furthermore, sufficient conditions represented as sum of squares (SOS), which can be solved by SOSTOOLS, are obtained based on a polynomial Lyapunov function. A numerical example is provided to demonstrate the effectiveness of the proposed method.