Stability of Neural Networks with Parameters Disturbed by White Noises

Abstract

Almost sure exponential stability (ASES) of neural networks with parameters disturbed by noises is studied, the basis of which is that the parameters in the implemented neural networks by very large scale integration (VLSI) approaches is well defined by the white-noise stochastic process, and an appropriate way to impose random factors on deterministic neural networks is proposed. By using the theory of stochastic dynamical system and matrix theory, some stability criteria are obtained which ensure the neural networks ASES, and the convergent rate is estimated. Also, the capacity of enduring random factors of the well-designed neural networks is estimated. The results obtained in this paper need only to compute the eigenvalues or verify the negative-definite of some matrices constructed by the parameters of the neural networks. An illustrative example is given to show the effectiveness of the results in the paper.