New necessary and sufficient conditions for absolute stability of neural networks

Authors:
Tianguang Chu;Cishen Zhang
Affiliations:
Intelligent Control Laboratory, Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing 100871, People's Republic of China;School of Electrical and Electronic Engineering and School of Chemical and Biomedical Engineering, Nanyang Technological University, Singapore 639798, Singapore
Venue:
Neural Networks
Year:
2007

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Abstract

This paper presents new necessary and sufficient conditions for absolute stability of asymmetric neural networks. The main result is based on a solvable Lie algebra condition, which generalizes existing results for symmetric and normal neural networks. An exponential convergence estimate of the neural networks is also obtained. Further, it is demonstrated how to generate larger sets of weight matrices for absolute stability of the neural networks from known normal weight matrices through simple procedures. The approach is nontrivial in the sense that non-normal matrices can possibly be contained in the resulting weight matrix set. And the results also provide finite checking for robust stability of neural networks in the presence of parameter uncertainties.