Necessary and sufficient condition for absolute stability of normal neural networks

Authors:
Tianguang Chu;Cishen Zhang;Zongda Zhang
Affiliations:
Department of Mechanics and Engineering Science, Center for Systems and Control, Peking University, Beijing 100871, People's Republic of China;School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore 639798;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
Venue:
Neural Networks
Year:
2003

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Abstract

Globally convergent dynamics of a class of neural networks with normal connection matrices is studied by using the Lyapunov function method and spectral analysis of the connection matrices. It is shown that the networks are absolutely stable if and only if all the real parts of the eigenvalues of the connection matrices are nonpositive. This extends an existing result on symmetric neural networks to a larger class including certain asymmetric networks. Further extension of the present result to certain non-normal case leads naturally to a quasi-normal matrix condition, which may be interpreted as a generalization of the so-called principle of detailed balance for the connection weights or the quasi-symmetry condition that was previously proposed in the literature in association with symmetric neural networks. These results are of particular interest in neural optimization and classification problems.