Abstract
Because of VLSI realization of artificial neural networks and measuring the elements of the circuits, noises coming from the circuits and the errors of the parameters of the network systems are therefore unavoidable. Making use of the stochastic version of Razumikhin theorem of stochastic functional differential equation, Lyapunov direct methods and matrix analysis,almost sure exponential stability on interval neural networks perturbed by white noises with time varying delays is examined, and some sufficient algebraic criteria which only depend on the systems’ parameters are given. For well designed deterministic neural networks, the results obtained in the paper also imply that how much tolerance against perturbation they have.
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References
Cao, J., Zhou, D.: Stability Analysis of Delayed Celluar Neural Networks. Neural Networks 11, 1601–1605 (1998)
Liao, X.: Robust Stability for Interval Hopfield Neural Networks with Time Delay. IEEE Tran. Neural Networks 9(5), 1042–1045 (1998)
Wang, J., Wu, G.: A Multilayer Recurrent Neural Network for Solving Continuous-Time Algebraic Riccati Equations. Neural Networks 11, 939–950 (1998)
Lu, H.: On Stability of Nonlinear Continuous-Time Neural Networks with Delays. Neural Networks 13, 1135–1143 (2000)
Liang, X., Wang, J.: A Proof of Kaszkurewicz and Byaya’s Conjecture on Absolute Stability of Neural Networks in Two-Neuron Case. IEEE Trans. Circuits and Systems-1: Fundamental Theory and Its Applications 47(4), 609–611 (2000)
Liao, X., Mao, X.: Stability of Stochastic Neural Networks. Neual, Parallel and Scientific Computations 14(4), 205–224 (1996)
Blythe, S., Mao, X.: Stability of Stochastic Delay Neural Networks. Journal of the Franklin Institute 338, 481–495 (2001)
Shen, Y., Liao, X.: Robust Stability of Nonlinear Stochastic Delayed Systems. Acta Automatica Sinic 25(4), 537–542 (1999)
Liao, X., Mao, X.: Exponential Stability of Stochastic Delay Interval Systems. Systems and Control Letters 40, 171–181 (2000)
Liao, W., Liao, X.: Robust Stability of Time-Delayed Interval CNN in Noisy Environment. Acta Automatica Sinic 30(2), 300–305 (2004)
Mao, X.: Stochastic Differential Equations and Their Applications, 1st edn. Horwood Pub, Chichester (1997)
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© 2006 Springer-Verlag Berlin Heidelberg
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Liao, W., Wang, Z., Liao, X. (2006). Almost Sure Exponential Stability on Interval Stochastic Neural Networks with Time-Varying Delays. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_24
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DOI: https://doi.org/10.1007/11759966_24
Publisher Name: Springer, Berlin, Heidelberg
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