A new Lyapunov functional approach to sampled-data synchronization control for delayed neural networks

• Published in: Journal of the Franklin Institute Vol. 355; no. 17; pp. 8857 - 8873
• Main Authors: Xiao, Shen-Ping, Lian, Hong-Hai, Teo, Kok Lay, Zeng, Hong-Bing, Zhang, Xiao-Hu
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.11.2018; Elsevier Science Ltd
• Subjects: Control systems design; Control theory; Finite element analysis; Linear matrix inequalities; Matrix methods; Neural networks; Parallel processing; Sampling; Synchronism
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2018.09.022

This paper discusses the problem of synchronization for delayed neural networks using sampled-data control. We introduce a new Lyapunov functional, called complete sampling-interval-dependent discontinuous Lyapunov functional, which can adequately capture sampling information on both intervals from r(t−τ¯) to r(tk−τ¯) and from r(t−τ¯) to r(tk+1−τ¯). Based on this Lyapunov functional and an improved integral inequality, less conservative conditions are derived to ensure the stability of the synchronization error system, leading to the fact that the drive neural network is synchronized with the response neural network. The desired sampled-data controller is designed in terms of solutions to linear matrix inequalities. A numerical example is provided to demonstrate that the proposed approaches are effective and superior to some existing ones in the literature.