Advertisement

Mean Square Exponential Stability of Hybrid Neural Networks with Uncertain Switching Probabilities

  • Xuyang Lou
  • Qian Ye
  • Ke Lou
  • Baotong Cui
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7390)

Abstract

This paper is concerned with the global exponential stability problem for a class of Markovian jumping recurrent neural networks (MJRNNs) with uncertain switching probabilities. The Markovian jumping recurrent neural networks under consideration involve parameter uncertainties in the mode transition rate matrix. By employing a Lyapunov functional, a linear matrix inequality (LMI) approach is developed to establish an easy-totest and delay-independent sufficient condition which guarantees that the dynamics of the neural network is globally exponentially stable in the mean square.

Keywords

Hybrid neural networks Markovian jumping exponential stability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yang, X., Liao, X., Tang, Y., et al.: Guaranteed Attractivity of Equilibrium Points in a Class of Delayed Neural Networks. International Journal of Bifurcation and Chaos 16(9), 2737–2743 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Di Marco, M., Grazzini, M., Pancioni, L.: Global Robust Stability Criteria for Interval Delayed Full-Range Cellular Neural Networks. IEEE Transactions on Neural Networks 22(4), 666–671 (2011)CrossRefGoogle Scholar
  3. 3.
    Joy, M.: Results Concerning the Absolute Stability of Delayed Neural Networks. Neural Networks 13, 613–616 (2000)CrossRefGoogle Scholar
  4. 4.
    Faydasicok, O., Arik, S.: Equilibrium and stability Analysis of Delayed Neural Networks under Parameter Uncertainties. Applied Mathematics and Computation 218(12), 6716–6726 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Sakthivel, R., Raja, R., Anthoni, S.M.: Exponential stability for Delayed Stochastic Bidirectional Associative Memory Neural Networks with Markovian Jumping and Impulses. Journal of Optimization Theory and Applications 150(1), 166–187 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Mahmoud, M.S., Xia, Y.Q.: Improved exponential Stability Analysis for Delayed Recurrent Neural Networks. Journal of the Franklin Institute-Engineering and Applied Mathematics 348(2), 201–211 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Ozcan, N.: A New Sufficient Condition for Global Robust Stability of Delayed Neural Networks. Neural Processing Letters 34(3), 305–316 (2011)CrossRefGoogle Scholar
  8. 8.
    Kovacic, M.: Timetable Construction with Markovian Neural Network. Eur. J. Oper. Res. 69(1), 92–96 (1993)zbMATHCrossRefGoogle Scholar
  9. 9.
    Tino, P., Cernansky, M., Benuskova, L.: Markovian Architectural Bias of Recurrent Neural Networks. IEEE Trans. Neural Networks 15(1), 6–15 (2004)CrossRefGoogle Scholar
  10. 10.
    Wang, Z.D., Liu, Y.R., Yu, L., Liu, X.H.: Exponential Stability of Delayed Recurrent Neural Networks with Markovian Jumping Parameters. Physics Letters A 356, 346–352 (2006)zbMATHCrossRefGoogle Scholar
  11. 11.
    Xie, L.: Stochastic Robust Stability Analysis for Markovian Jumping Neural Networks with Time Delays, Networking. In: Proceedings IEEE Sensing and Control, pp. 923–928, March 19-22 (2005)Google Scholar
  12. 12.
    Lu, Y., Ren, W., Yi, S., et al.: Stability Analysis for Discrete Delayed Markovian Jumping Neural Networks with Partly Unknown Transition Probabilities. Neurocomputing 74(18), 3768–3772 (2011)CrossRefGoogle Scholar
  13. 13.
    Lou, X.Y., Cui, B.T.: Stochastic Exponential Stability for Markovian Jumping BAM Neural Networks with Time-Varying Delays. IEEE Trans. Systems, Man and Cybernetics-Part B. 37(3), 713–719 (2007)CrossRefGoogle Scholar
  14. 14.
    Xiong, J.L., Lam, J., Gao, H.J., Ho, D.W.C.: On Robust Stabilization of Markovian Jumpsystems with Uncertain Switching Probabilities. Automatica 41, 897–903 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Mahmoud, M.S., Shi, P.: Robust Stability, Stabilization and H Control of Time-delay Systems with Markovian Jump Parameters. Int. J. Robust Nonlinear Control 13, 755–784 (2003)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Xuyang Lou
    • 1
  • Qian Ye
    • 1
  • Ke Lou
    • 1
  • Baotong Cui
    • 1
  1. 1.Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education)Jiangnan UniversityWuxiChina

Personalised recommendations