Global asymptotic and robust stability of recurrent neural networks with time delays

• Published in: IEEE transactions on circuits and systems. I, Regular papers Vol. 52; no. 2; pp. 417 - 426
• Main Authors: Cao, Jinde, Wang, Jun
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2005; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic stability; Delay effects; Global asymptotic stability (GAS); global robust stability (GRS); interval neural network; Linear matrix inequalities; linear matrix inequality (LMI); Lyapunov functional; Lyapunov method; matrix inequality; Neural networks; Neurons; Recurrent neural networks; Robust stability; Stability criteria; Sufficient conditions; time delay
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2004.841574

In this paper, two related problems, global asymptotic stability (GAS) and global robust stability (GRS) of neural networks with time delays, are studied. First, GAS of delayed neural networks is discussed based on Lyapunov method and linear matrix inequality. New criteria are given to ascertain the GAS of delayed neural networks. In the designs and applications of neural networks, it is necessary to consider the deviation effects of bounded perturbations of network parameters. In this case, a delayed neural network must be formulated as a interval neural network model. Several sufficient conditions are derived for the existence, uniqueness, and GRS of equilibria for interval neural networks with time delays by use of a new Lyapunov function and matrix inequality. These results are less restrictive than those given in the earlier references.