A novel polynomial membership functions based control method for T–S fuzzy systems. (October 2022) - Xie, Wen-Bo; Zhang, Jian; Li, Yi-Fan; Palhares, Reinaldo M.
Abstract: To solve the state feedback stabilization problem for a class of T–S fuzzy systems, a new stability synthesis method is raised to further relax the conservatism existing in the analysis process. First, a series of nonlinear polynomials are used to approximate the system membership functions. And satisfied approximation results can be obtained. Then a polynomials transformation method is raised to change the polynomial membership functions into linear form. This method can facilitate the synthesis process and achieve better approximation precision. Therefore, by a membership function involving stability analysis approach, linear matrix inequality form stability conditions are given. Finally, by presenting and analyzing a numerical and a practical examples, the conservatism reduction effects of the proposed methods are verified. Highlights: Membership approximating polynomials are changed into multi-dimensional linear form SOS conditions are replaced by locally valid LMI conditions Globally valid SOS method is avoided, stability conservatism is efficiently reduced