Novel stability criteria of generalized neural networks with time-varying delay based on the same augmented LKF and bounding technique

• Published in: Applied mathematics and computation 2024-01, Vol.460, p.128289, Article 128289
• Main Authors: Zhai, Zhengliang, Yan, Huaicheng, Chen, Shiming, Chang, Yufang, Zhou, Jing
• Format: Article
• Language: English
• Subjects: Generalized neural networks; Negative definite conditions; Third order integral inequality; Time-varying delay
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2023.128289

This paper researches the stability issue of generalized neural networks (GNN) with time-varying delay. For the delay, its derivative has an upper bound or is unknown. Firstly, the augmented Lyapunov-Krasovskii functional (LKF) is constructed based on the state vectors of the third order integral inequalities. Then, by introducing two sets of state vectors, the LKF derivative is presented as the quadratic and quintic polynomials of the delay, respectively. Next, the new quadratic and quintic polynomial negative definite conditions (NDCs) are proposed to set up the linear matrix inequalities (LMIs). In addition, based on the same LKF and third order integral inequalities, this paper proves that the introduction of extra state vectors increases the conservatism of the derived stability conditions. Eventually, the advantages of the provided conditions are illustrated by several numerical examples. •Based on the third order FMBIIs, the novel augmented LKF is constructed.•The LKF derivative is presented as the quadratic and quintic polynomials, respectively.•For the quadratic and quintic polynomials, the novel NDCs are provided.•This paper proves that the introduction of extra state vectors increases the conservativeness of the stability conditions.