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Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network

Author

Listed:
  • Zixin Liu
  • Jian Yu
  • Daoyun Xu
  • Dingtao Peng

Abstract

On the basis of the fact that the neuron activation function is sector bounded, this paper transforms the researched original delayed neural network into a linear uncertain system. Combined with delay partitioning technique, by using the convex combination between decomposed time delay and positive matrix, this paper constructs a novel Lyapunov function to derive new less conservative stability criteria. The benefit of the method used in this paper is that it can utilize more information on slope of the activations and time delays. To illustrate the effectiveness of the new established stable criteria, one numerical example and an application example are proposed to compare with some recent results.

Suggested Citation

  • Zixin Liu & Jian Yu & Daoyun Xu & Dingtao Peng, 2013. "Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:710741
    DOI: 10.1155/2013/710741
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    References listed on IDEAS

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    1. Cho, Hyun J. & Park, Ju H., 2007. "Novel delay-dependent robust stability criterion of delayed cellular neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1194-1200.
    2. J.M. da Silva & A. Seuret & E. Fridman & J.P. Richard, 2011. "Stabilisation of neutral systems with saturating control inputs," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(7), pages 1093-1103.
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