Stability Analysis for Delayed Neural Networks via a Generalized Reciprocally Convex Inequality

• Published in: IEEE transaction on neural networks and learning systems Vol. 34; no. 10; pp. 7491 - 7499
• Main Authors: Lin, Hui-Chao, Zeng, Hong-Bing, Zhang, Xian-Ming, Wang, Wei
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.10.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Artificial neural networks; Delayed neural network (NN); Delays; Linear matrix inequalities; Lyapunov-Krasovskii functional (LKF); Neural networks; Neurons; reciprocally convex combination; Stability analysis; Stability criteria; Symmetric matrices; Time-varying systems
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2022.3144032

This article deals with the stability of neural networks (NNs) with time-varying delay. First, a generalized reciprocally convex inequality (RCI) is presented, providing a tight bound for reciprocally convex combinations. This inequality includes some existing ones as special case. Second, in order to cater for the use of the generalized RCI, a novel Lyapunov-Krasovskii functional (LKF) is constructed, which includes a generalized delay-product term. Third, based on the generalized RCI and the novel LKF, several stability criteria for the delayed NNs under study are put forward. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the proposed stability criteria.