Stability of Stochastic Recurrent Neural Networks with Positive Linear Activation Functions

In view of the character of positive linearity of activation functions of neurons of the recurrent neural networks, the method decomposing the state space to sub-regions is adopted to study almost sure exponential stability on delayed cellular neural networks which are in the noised environment. When perturbed terms in the model of the neural network satisfy Lipschitz condition, some algebraic criteria are obtained. The results obtained in this paper show that if an equilibrium of the neural network is the interior point of a sub-region, and an appropriate matrix related to this equilibrium has some stable degree to stabilize the perturbation, then the equilibrium of the delayed cellular neural network can still remain the property of exponential stability. All results in the paper is only to compute eigenvalues of matrices. All results obtained in this paper include the deterministic neural network as special case.

Authors and Affiliations

1. School of Electrical and Information Engineering, Zhongyuan University of Technology, Zhengzhou, 450007, China

   Wudai Liao & Xuezhao Yang

2. School of Information Engineering, Guangdong Polytechnic Normal University, Guangzhou, 510665, China

   Zhongsheng Wang

Editors and Affiliations

1. Departamento de Control Automático, CINVESTAV-IPN, A.P. 14-740, Av.IPN 2508, 07360, México D.F., México

   Wen Yu

2. Deptartment of Electrical and Computer Engineering, Stevens Institute of Technology, NJ 07030, Hoboken, USA

   Haibo He

3. Dept. of Electrical and Computer Engineering, South Dakota School of Mines & Technology, 501 E. St. Joseph Street, Rapid City, SD 57701, USA

   Nian Zhang

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