A Polynomial Membership Function Approach for Stability Analysis of Fuzzy Systems

For the stability analysis of a polynomial fuzzy system, a new polynomial membership function approach is proposed to reduce conservatism. In this article, based on a state-feedback closed-loop system, a polynomials fitting method is utilized, and an improved membership function transformation technique is proposed to approximate the membership functions of the fuzzy system. Then, the membership-function-dependent polynomial-based stability conditions are derived. The obtained polynomial membership functions and approximation errors will be involved in the stability analysis process. Based on the sum-of-squares optimization technique, polynomial conditions can be directly solved. Finally, by several numerical and practical examples, conservatism reduction effects are shown by comparisons with existing methods.

Automated summary

A new polynomial membership function approach is proposed for stability analysis of polynomial fuzzy systems, utilizing fitting methods and transformation techniques to reduce conservatism. The derived polynomial-based stability conditions are used in the analysis process, with direct solutions through sum-of-squares optimization technique, showcasing conservatism reduction effects through numerical and practical examples.