Algebra criteria for global exponential stability of multiple time-varying delay Cohen–Grossberg neural networks

• Published in: Applied mathematics and computation 2022-12, Vol.435, p.127461, Article 127461
• Main Authors: Zhang, Zhongjie, Yu, Tingting, Zhang, Xian
• Format: Article
• Language: English
• Subjects: Algebra Criteria; Cohen–Grossberg neural networks; Global exponential stability; Lyapunov–Krasovskii functionals; Multiple time-varying delays
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2022.127461

•The proposed method is applicable to Cohen-Grossberg neural networks that can or can not be written as the vector-matrix form.•The second and third terms in the Lyapunov-Krasovskii functionals are introduced for the first time.•The algebraic criteria are given for the first time. This paper aims at establishing global exponential stability criteria for multiple time-varying delay Cohen–Grossberg neural networks (CGNNs). The considered network models cannot be expressed as the vector-matrix form, which yields that many methods in literature are unavailable. By constructing novel Lyapunov–Krasovskii functionals, two novel algebraic criteria guaranteeing global exponential stability of CGNNs under consideration are given. A pair of numerical examples are used to explain the effectiveness of the obtained algebra criteria relative to the previously stability conditions. It is worth emphasizing that the approach applied in this paper is applicable to CGNNs that may or may not be represented in vector-matrix form.