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Neural Processing Letters

, Volume 41, Issue 1, pp 1–27 | Cite as

Robust Stability of Markovian Jump Stochastic Neural Networks with Time Delays in the Leakage Terms

  • Quanxin Zhu
  • Jinde Cao
  • Tasawar Hayat
  • Fuad Alsaadi
Article

Abstract

This paper deals with the problem of exponential stability for a class of Markovian jump stochastic neural networks with time delays in the leakage terms and mixed time delays. The jumping parameters are modeled as a continuous-time, finite-state Markov chain, and the mixed time delays consist of time-varying delays and distributed delays. By using the method of model transformation, Lyapunov stability theory, stochastic analysis and linear matrix inequalities techniques, several novel sufficient conditions are derived to guarantee the exponential stability in the mean square of the equilibrium point of the suggested system in two cases: with known or unknown parameters. Moreover, some remarks and discussions are given to illustrate that the obtained results are significant, which comprises and generalizes those obtained in the previous literature. In particular, the obtained stability conditions are delay-dependent, which depends on all the delay constants, and thus the presented results are less conservatism. Finally, two numerical examples are provided to show the effectiveness of the theoretical results.

Keywords

Exponential stability Stochastic neural network Lyapunov functional Linear matrix inequality Markovian jump parameter Leakage time delay 

Notes

Acknowledgments

This work was jointly supported by the National Natural Science Foundation of China (61374080, 61272530, 11072059), the Natural Science Foundation of Zhejiang Province (LY12F03010), the Natural Science Foundation of Ningbo (2012A610032), the Natural Science Foundation of Jiangsu Province (BK2012741), the Specialized Research Fund for the Doctoral Program of Higher Education (20110092110017,20130092110017), the Deanship of Scientific Research (DSR), King Abdulaziz University (KAU), under Grant 3-130/1434/HiCi.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Quanxin Zhu
    • 1
  • Jinde Cao
    • 2
    • 4
  • Tasawar Hayat
    • 3
    • 4
  • Fuad Alsaadi
    • 5
  1. 1.School of Mathematical Sciences and Institute of Finance and StatisticsNanjing Normal UniversityNanjing China
  2. 2.Department of Mathematics and Research Center for Complex Systems and Network SciencesSoutheast UniversityNanjing China
  3. 3.Department of MathematicsQuaid-I-Azam UniversityIslamabad Pakistan
  4. 4.Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  5. 5.Department of Electrical and Computer Engineering, Faculty of EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia

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