Global exponential stability of generalized recurrent neural networks with discrete and distributed delays

Authors:
Yurong Liu;Zidong Wang;Xiaohui Liu
Affiliations:
Department of Mathematics, Yangzhou University, Yangzhou 225002, People's Republic of China;Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex UB8 3PH, UK;Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex UB8 3PH, UK
Venue:
Neural Networks
Year:
2006

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Abstract

This paper is concerned with analysis problem for the global exponential stability of a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. We first prove the existence and uniqueness of the equilibrium point under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, by employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the RNNs to be globally exponentially stable. Therefore, the global exponential stability of the delayed RNNs can be easily checked by utilizing the numerically efficient Matlab LMI toolbox, and no tuning of parameters is required. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.