Global exponential stability criteria for neural networks with probabilistic delays

Author(s): M.S. Mahmoud ; S.Z. Selim ; P. Shi
DOI: 10.1049/iet-cta.2009.0007

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Author(s): M.S. Mahmoud ¹ ; S.Z. Selim ¹ ; P. Shi ^{2, 3}
- Affiliations: 1: Systems Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
  2: Department of Computing and Mathematical Sciences, University of Glamorgan, Pontypridd, UK
  3: Department of Computing and Mathematical Sciences, Victoria University, ILSCM, School of Science and Engineering and University of South Australia, School of Mathematics and Statistics, Australia
Source: Volume 4, Issue 11, November 2010, p. 2405 – 2415
DOI: 10.1049/iet-cta.2009.0007 , Print ISSN 1751-8644, Online ISSN 1751-8652

The problem of global exponential stability analysis for a class of neural networks (NNs) with probabilistic delays is discussed in this paper. The delay is assumed to follow a given probability density function. This function is discretised into arbitrary number of intervals. In this way, the NN with random time delays is transformed into one with deterministic delays and random parameters. New conditions for the exponential stability of such NNs are obtained by employing new Lyapunov–Krasovskii functionals and novel techniques for achieving delay dependence. It is established that these conditions reduce the conservatism by considering not only the range of the time delays, but also the probability distribution of their variation. Numerical examples are provided to show the advantages of the proposed techniques.

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Global exponential stability criteria for neural networks with probabilistic delays

Global exponential stability criteria for neural networks with probabilistic delays

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