Stability Analysis for Delayed Neural Networks Considering Both Conservativeness and Complexity

• Published in: IEEE transaction on neural networks and learning systems Vol. 27; no. 7; pp. 1486 - 1501
• Main Authors: Zhang, Chuan-Ke, He, Yong, Jiang, Lin, Wu, Min
• Format: Journal Article
• Language: English
• Published: United States IEEE 01-07-2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Biological neural networks; Calculation complexity; Complexity; Complexity theory; conservativeness; Criteria; Delay; delay-dependent stability; delayed neural networks (DNNs); Delays; Derivatives; Guidelines; Lyapunov-Krasovskii functional (LKF); Mathematical analysis; Neural networks; Numerical stability; Stability; Stability criteria; Symmetric matrices; delay-dependent stability; conservativeness; Lyapunov–Krasovskii functional (LKF); Calculation complexity; delayed neural networks (DNNs)
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2015.2449898

This paper investigates delay-dependent stability for continuous neural networks with a time-varying delay. This paper aims at deriving a new stability criterion, considering tradeoff between conservativeness and calculation complexity. A new Lyapunov-Krasovskii functional with simple augmented terms and delay-dependent terms is constructed, and its derivative is estimated by several techniques, including free-weighting matrix and inequality estimation methods. Then, the influence of the techniques used on the conservativeness and the complexity is analyzed one by one. Moreover, useful guidelines for improving criterion and future work are briefly discussed. Finally, the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples.