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Stochastic Robust Stability Analysis for Markovian Jump Discrete-Time Delayed Neural Networks with Multiplicative Nonlinear Perturbations

  • Li Xie
  • Tianming Liu
  • Guodong Lu
  • Jilin Liu
  • Stephen T. C. Wong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3971)

Abstract

The problem of stochastic robust stability for Markovian jump discrete-time delayed neural networks with multiplicative nonlinear perturbation is investigated via Lyapunov stability theory in this paper. Based on the linear matrix inequality (LMI) methodology, a novel analysis approach is developed. The sufficient conditions of stochastically robust stable are given in terms of coupled linear matrix inequalities. The stable criteria represented in LMI setting are less conservative and more computationally efficient than the methods reported in the literature.

Keywords

Linear Matrix Inequality Recurrent Neural Network Markovian Jump Bidirectional Associative Memory Lyapunov Stability Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Michel, A.N., Farrell, J.A., Porod, W.: Qualitative Analysis of Neural Networks. IEEE Trans. CAS 36(2), 229–243 (1989)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Kelly, D.G.: Stability in Contractive Nonlinear Neural Networks. IEEE Trans. Bio. Eng. 37(3), 231–242 (1990)CrossRefGoogle Scholar
  3. 3.
    Liang, X.B., Wang, J.: An Additive Diagonal Stability Condition for Absolute Exponential Stability of a General Class of Neural Networks. IEEE Trans. CAS—I 48, 1308–1317 (2001)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Cao, J., Wang, J.: Global Asymptotic and Robust Stability of Recurrent Neural Networks with Time Delays. IEEE Trans. CAS—I 52(2), 417–426 (2005)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Liao, X., Wong, K.W.: Robust Stability of Interval Bidirectional Associative Memory Neural Network With Time Delays. IEEE Trans. SMC—B 34(2), 1142–1154 (2004)Google Scholar
  6. 6.
    Feng, C.H., Plamondon, R.: Stability Analysis of Bidirectional Associative Memory NetWorks with Time Delays. IEEE Trans. NN 14(6), 1560–1565 (2003)Google Scholar
  7. 7.
    Ji, Y., Chizeck, H.J.: Controllability, Stabilizability, and Continuous-Time Markovian Jump Linear Quadratic Control. IEEE Trans. AC 35(7), 777–788 (1990)MATHMathSciNetGoogle Scholar
  8. 8.
    Feng, X., Loparo, K.A., Ji, Y., et al.: Stochastic Stability Properties of Jump Linear System. IEEE Trans. AC 37(1), 38–53 (1992)MATHMathSciNetGoogle Scholar
  9. 9.
    Liao, X., Chen, G.R., Sanchez, E.N.: LMI-Based Approach for Asymptotically Stability Analysis of Delayed Neural Networks. IEEE Trans. CAS-I 49(7), 1033–1039 (2002)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Li Xie
    • 1
  • Tianming Liu
    • 3
  • Guodong Lu
    • 2
  • Jilin Liu
    • 1
  • Stephen T. C. Wong
    • 3
  1. 1.Department of Information and Electronic EngineeringZhejiang University 
  2. 2.State Key Lab of CAD & CGZhejiang UniversityHangzhouP.R. China
  3. 3.Center for Bioinformatics, HCNRHarvard Medical SchoolBostonUSA

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