Relaxed Stability and Non-weighted L2-Gain Analysis for Asynchronously Switched Polynomial Fuzzy Systems

• Published in: International journal of fuzzy systems Vol. 27; no. 5; pp. 1373 - 1389
• Main Authors: Bao, Zhiyong, Lam, Hak-Keung, Li, Xiaomiao, Liu, Fucai
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2025; Springer Nature B.V
• Subjects: Artificial Intelligence; Computational Intelligence; Dwell time; Engineering; Fuzzy sets; Fuzzy systems; L2 gain; Liapunov functions; Management Science; Mathematical functions; Operations Research; Polynomials; Stability criteria; Systems stability; High-order multiple Lyapunov functions (MLFs); Stability analysis; Asynchronously switched polynomial fuzzy systems; gain analysis; Non-weighted
• ISSN: 1562-2479; 2199-3211
• DOI: 10.1007/s40815-024-01840-x

This paper concerns the stability and non-weighted L 2 -gain analysis issues for the switched systems subject to asynchronous switching and external disturbance. By taking full advantage of the admissible edge-dependent average dwell time (AED-ADT) switching signal, a stability criterion of asynchronously switched systems is proposed to achieve a lower non-weighted L 2 -gain index than the existing results. Furthermore, the dynamics of switched systems are described by using the polynomial fuzzy model instead of the T-S fuzzy model, which can represent a wider range of nonlinear plants. For such asynchronously switched polynomial fuzzy systems, the relaxed conditions are derived through the membership-function-dependent (MFD) technique and novel high-order multiple Lyapunov functions (MLFs) construction method to guarantee less conservative stability and non-weighted L 2 -gain results. Finally, the superiority of the proposed approaches are verified through two simulation examples.