LMI Based Global Asymptotic Stability Criterion for Recurrent Neural Networks with Infinite Distributed Delays

Authors:
Zhanshan Wang;Huaguang Zhang;Derong Liu;Jian Feng
Affiliations:
School of Information Science and Engineering, Northeastern University, Shenyang, People's Republic of China 110004;School of Information Science and Engineering, Northeastern University, Shenyang, People's Republic of China 110004;Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, USA IL60607;School of Information Science and Engineering, Northeastern University, Shenyang, People's Republic of China 110004
Venue:
ISNN '09 Proceedings of the 6th International Symposium on Neural Networks on Advances in Neural Networks
Year:
2009

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Abstract

Global asymptotic stability problem for a class of recurrent neural networks with infinite distributed delay is investigated based on the linear matrix inequality (LMI) technique. Using a matrix decomposition method, a vector-matrix form of recurrent neural networks with infinite distributed delay is obtained. Then by constructing a suitable Lyapunov functional and using an inequality, new LMI-based criteria are established to ensure the global asymptotic stability of the class of neural networks, which considers the effects of neuron's excitatory and inhibitory action in the term of infinite delay on the networks. The obtained results are independent of the size of delay and are easily verified. Numerical example shows the effectiveness of the obtained results.