, Volume 28, Issue 4, pp 505-522

New Stability Criteria for Neural Networks with Distributed and Probabilistic Delays

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Abstract

This paper is concerned with the stability analysis of neural networks with distributed and probabilistic delays. The probabilistic delay satisfies a certain probability distribution. By introducing a stochastic variable with a Bernoulli distribution, the neural network with random time delays is transformed into one with deterministic delays and stochastic parameters. New conditions for the exponential stability of such neural networks are obtained by employing new Lyapunov–Krasovskii functionals and novel techniques for achieving delay dependence. The proposed conditions reduce the conservatism by considering not only the range of the time delays, but also the probability distribution of their variation. A numerical example is provided to show the advantages of the proposed techniques.

This work was partially supported by National Natural Science Foundation of China (60528007 and 60825303), the Research Fund for the Doctoral Programme of Higher Education of China (20070213084), RGC HKU 7028/04P, Hong Kong, China, and EPSRC (EP/F029195), UK.