Enhanced cubic function negative-determination Lemma on stability analysis for delayed neural networks via new analytical techniques

• Published in: Journal of the Franklin Institute Vol. 361; no. 3; pp. 1155 - 1166
• Main Authors: Leng, Jiahao, Wang, Jun, Shi, Kaibo, Cheng, Jun, Wen, Shiping, Tang, Yiqian
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-02-2024
• Subjects: Asymmetric Lyapunov–Krasovskii functional; Enhanced cubic functions; Negative-definiteness determination; Neural networks; Partitioning technique; Enhanced cubic functions; Negative-definiteness determination; Asymmetric Lyapunov–Krasovskii functional; Neural networks; Partitioning technique
• ISSN: 0016-0032
• DOI: 10.1016/j.jfranklin.2024.01.007

This brief studies the stability issue of neural networks with respect to time-varying delay. First, an enhanced cubic functions negative-definiteness determination Lemma is proposed by using partitioning technique and Taylor’s formula. Compared with the previous results, this Lemma can eliminate the conservatism of constraint conditions by interval-decomposition method. Second, for the sake of the relaxed positive-definiteness determination, an asymmetric Lyapunov–Krasovskii functional is presented. Third, a resulting time-varying delay-dependent stability criterion is derived by making use of some inequality techniques. Finally, the advantage of the new approach are verified theoretically and numerically.