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Stability analysis of discrete-time recurrent neural networks based on standard neural network models

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Abstract

In order to conveniently analyze the stability of various discrete-time recurrent neural networks (RNNs), including bidirectional associative memory, Hopfield, cellular neural network, Cohen-Grossberg neural network, and recurrent multiplayer perceptrons, etc., the novel neural network model, named standard neural network model (SNNM) is advanced to describe this class of discrete-time RNNs. The SNNM is the interconnection of a linear dynamic system and a bounded static nonlinear operator. By combining Lyapunov functional with S-Procedure, some useful criteria of global asymptotic stability for the discrete-time SNNMs are derived, whose conditions are formulated as linear matrix inequalities. Most delayed (or non-delayed) RNNs can be transformed into the SNNMs to be stability analyzed in a unified way. Some application examples of the SNNMs to the stability analysis of the discrete-time RNNs shows that the SNNMs make the stability conditions of the RNNs easily verified.

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Authors and Affiliations

  1. Department of System Science and Engineering, College of Electrical Engineering, Zhejiang University, 310027, Hangzhou, People’s Republic of China

    Meiqin Liu

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  1. Meiqin Liu
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Correspondence to Meiqin Liu.

Additional information

This work was supported in part by the National Natural Science Foundation of China under Grant 60504024 and 60874050, in part by the Zhejiang Provincial Natural Science Foundation of China under Grant Y106010, and in part by the Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP), China under Grant 20060335022. This work was also supported by the “151 Talent Project” of Zhejiang Province (No. 05-3-1013 and No. 06-2-034).

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Liu, M. Stability analysis of discrete-time recurrent neural networks based on standard neural network models. Neural Comput & Applic 18, 861–874 (2009). https://doi.org/10.1007/s00521-008-0211-5

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