Journal
IEEE TRANSACTIONS ON FUZZY SYSTEMS
Volume 29, Issue 8, Pages 2077-2087Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2020.2991149
Keywords
Fuzzy systems; Lyapunov methods; Numerical stability; Approximation error; Stability criteria; Conservatism; polynomial fuzzy system; polynomial membership functions (PLMFs); sum of squares (SOS)
Funding
- Natural Science Foundation in Heilongjiang Province, China [YQ2019F012]
- Postdoctoral Science Foundation of China [2019M661463]
- University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province, China [UNPYSCT-2017093]
- National Natural Science Foundation of China [61803127, 61803114]
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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.
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.
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