Circuits, Systems & Signal Processing

, Volume 28, Issue 4, pp 505–522

New Stability Criteria for Neural Networks with Distributed and Probabilistic Delays


DOI: 10.1007/s00034-008-9092-1

Cite this article as:
Yang, R., Gao, H., Lam, J. et al. Circuits Syst Signal Process (2009) 28: 505. doi:10.1007/s00034-008-9092-1


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.


Distributed delayExponential stabilityNeural networksLyapunov–Krasovskii functionalTime-varying delay

Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Rongni Yang
    • 1
  • Huijun Gao
    • 1
  • James Lam
    • 2
  • Peng Shi
    • 3
    • 4
    • 5
  1. 1.Space Control and Inertial Technology Research CenterHarbin Institute of TechnologyHarbinChina
  2. 2.Department of Mechanical EngineeringUniversity of Hong KongHong KongChina
  3. 3.Faculty of Advanced TechnologyUniversity of GlamorganPontypriddUK
  4. 4.Institute for Logistics and Supply Chain Management, School of Computer Science and MathematicsVictoria UniversityMelbourneAustralia
  5. 5.School of Mathematics and StatisticsUniversity of South AustraliaAdelaideAustralia