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Science China Technological Sciences

, Volume 59, Issue 3, pp 387–402 | Cite as

Exponential H filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities

  • JinDe CaoEmail author
  • R. Rakkiyappan
  • K. Maheswari
  • A. Chandrasekar
Article

Abstract

This paper is concerned with the exponential H filtering problem for a class of discrete-time switched neural networks with random time-varying delays based on the sojourn-probability-dependent method. Using the average dwell time approach together with the piecewise Lyapunov function technique, sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with random time-varying delays which are characterized by introducing a Bernoulli stochastic variable. Based on the derived H performance analysis results, the H filter design is formulated in terms of Linear Matrix Inequalities (LMIs). Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed design procedure.

Keywords

switched neural networks average dwell time sojourn probability method exponential stability 

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References

  1. 1.
    Kwon O M, Park J H. New delay-dependent robust stability criteria for uncertain neural networks with time-varying delay. Appl Math Comput, 2008, 205: 417–427MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Cao J, Wang J. Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delay. Neural Networks, 2004, 17: 379–390CrossRefzbMATHGoogle Scholar
  3. 3.
    Arik S. An analysis of exponential stability of delayed neural networks with time-varying delays. Neural Networks, 2004, 17: 1027–1031CrossRefzbMATHGoogle Scholar
  4. 4.
    Zhang H, Liu Z, Huang G. Novel delay-dependent robust stability analysis for switched neutral-type neural networks with time-varying delays via SC technique. IEEE T Syst Cy, 2010, 40: 1480–1491CrossRefGoogle Scholar
  5. 5.
    Song Z, Xu J. Stability switches and Bogdanov-Takens bifurcation in an inertial two-neuron coupling system with multiple delays. Sci China Tech Sci, 2014, 57: 893–904CrossRefGoogle Scholar
  6. 6.
    Jiao X, Zhu D. Phase-response synchronization in neuronal population. Sci China Tech Sci, 2014, 57: 923–928CrossRefGoogle Scholar
  7. 7.
    Qin H, Ma J, Jin W, et al. Dynamics of electric activities in neuron and neurons of network induced by autapses. Sci China Tech Sci, 2014, 57: 936–946CrossRefGoogle Scholar
  8. 8.
    Song X, Wang C, Ma J, et al. Transition of electric activity of neurons induced by chemical and electric autapses. Sci China Tech Sci, 2015, 58: 1007–1014CrossRefGoogle Scholar
  9. 9.
    Cao J, Sivasamy R, Rakkiyappan R. Sampled-Data H synchronization of Chaotic Lur’e systems with time delay. Circ Syst Signal Pr, 2015, doi: 10.1007/s00034-015-0105-6Google Scholar
  10. 10.
    Rakkiyappan R, Sakthivel N, Cao J. Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Neural Networks, 2015, 66: 46–63CrossRefGoogle Scholar
  11. 11.
    Wu L, Zheng W X. Weighted H model reduction for linear switched systems with time-varying delay. Automatica, 2009, 45: 186–193MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Sun Z, Ge S. Stability Theory of Switched Dynamical Systems. Springer Verlag, 2011CrossRefzbMATHGoogle Scholar
  13. 13.
    Jeong C, Park P, Kim S H. Improved approach to robust stability and H performance analysis for systems with an interval time-varying delay. Appl Math Comput, 2012, 218: 10533–10541MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Wei G, Wang Z, Lam J, et al. Robust filtering for stochastic genetic regulatory networks with time-varying delay. Math Biosci, 2009, 220: 73–80MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Balasubramaniam P, Krishnasamy R, Rakkiyappan R. Delaydependent stability of neutral systems with time varying delays using delay-decomposition approach. Appl Math Model, 2012, 36: 2253–2261MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Liang J, Wang Z, Liu X. State estimation for coupled uncertain stochastic networks with missing measurements and time varying delays: The discrete case. IEEE T Neural Networ, 2009, 20: 781–793CrossRefGoogle Scholar
  17. 17.
    Lakshmanan S, Park J H, Jung H Y, et al. Design of state estimator for neural networks with leakage, discrete and distributed delays. Appl Math Comput, 2012, 218: 11297–11310MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Kwon O M, Park M J, Lee S M, et al. Stability for neural networks with time-varying delaying via some new approaches. IEEE T Neural Networ, 2013, 24: 181–193Google Scholar
  19. 19.
    Kwon O M, Lee S M, Park J H, et al. New approaches on stability criteria for neural networks with interval time-varying delays. Appl Math Comput, 2012, 218: 9953–9964MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Kim D K, Park P G, Ko J W. Output-feedback H control of systems over communication networks using deterministic switching system approach. Automatica, 2004, 40: 1205–1212MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Wu L, Zhiguang F, Lam J. Stability and synchronization of discretetime neural networks with switching parameters and time-varying delays. IEEE T Neural Networ, 2013, 24: 1957–1972Google Scholar
  22. 22.
    Wu X, Tang Y, Zhang W. Stability analysis of switched stochastic neural networks with time-varying delays. Neural Networks, 2014, 51: 39–49CrossRefzbMATHGoogle Scholar
  23. 23.
    Ishii H, Francis B A. Stabilizing a linear system by switching control with dwell time. IEEE T Automat Cont, 2002, 47: 1962–1973MathSciNetCrossRefGoogle Scholar
  24. 24.
    Yao Y, Liang J, Cao J. Stability analysis for switched genetic regulatory networks: An average dwell time approach. J Franklin Inst, 2011, 348: 2718–2733MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Wu L, Zheng W X. H model reduction for switched hybrid systems with time-varying delay. Automatica, 2009, 45: 186–193MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Wu L, Feng Z, Zheng W X. Exponential stability analysis for delayed neural networks with switching parameters: average dwell time approach. IEEE T Neural Networ, 2010, 21: 1396–1407CrossRefGoogle Scholar
  27. 27.
    Hu M, Cao J, Hu A. Mean square exponential stability for discretetime stochastic switched static neural networks with randomly occurring nonlinearities and stochastic delay. Neurocomputing, 2014, 129: 476–481CrossRefGoogle Scholar
  28. 28.
    Hou L, Zong G, Wu L. Robust stability analysis of discrete-time switched Hopfield neural networks with time delay. Nonlinear Anal Hybird Syst, 2011, 5: 525–534MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Wu Z, Shi P, Su H, et al. Delay dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay. Neurocomputing, 2011, 74: 1626–1631CrossRefGoogle Scholar
  30. 30.
    Mathiyalagan K, Sakthivel R, Marshal Anthoni S. New robust exponential stability results for discrete -time switched fuzzy neural networks with time delays. Computers and Mathematics with Applications, 2012, 64: 2926–2938MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Wang Z, Ho D W C, Liu X. State estimation for delayed neural networks. IEEE T Neural Networ, 2005, 16: 279–284CrossRefGoogle Scholar
  32. 32.
    Bao H, Cao J. Delay-distribution-dependent state estimation for discrete time stochastic neural networks with random delay. Neural Networks, 2011, 24: 19–28CrossRefzbMATHGoogle Scholar
  33. 33.
    Balasubramaniam P, Jarina B L. Robust state estimation for discretetime genetic regulatory network with random delay. Neurocomputing, 2013, 122: 349–369CrossRefGoogle Scholar
  34. 34.
    Tang Y, Fang J, Xia M, et al. Delay-distribution-dependent stability of stochastic discrete-time neural networks with randomly mixed timevarying delays. Neurocomputing, 2009, 72: 3830–3838CrossRefGoogle Scholar
  35. 35.
    Zhang Y, Yue D, Tian E. Robust delay-distribution-dependent stability of discrete-time stochastic neural networks with time-varying delay, Neurocomputing, 2009, 72: 1265–1273Google Scholar
  36. 36.
    Tian E, Wong W K, Yue D. Robust H control for switched systems with input delays: A sojourn-probability-dependent method. Inform Sci, 2014, 283: 22–35MathSciNetCrossRefGoogle Scholar
  37. 37.
    Tian E, Yue D, Yang T. Analysis and synthesis of randomly switched systems with known sojourn probabilities. Inform Sci, 2014, 277: 481–491MathSciNetCrossRefGoogle Scholar
  38. 38.
    Liu Y, Wang Z, Liu X. Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Networks, 2006, 19: 667–675CrossRefzbMATHGoogle Scholar
  39. 39.
    Wang T, Xue M, Fei S, et al. Triple Lyapunov functional technique on delay dependent stability for discrete time dynamical network. Neurocomputing, 2013, 122: 221–228CrossRefGoogle Scholar
  40. 40.
    Park P, Ko J W, Jeong C. Reciprocally convex approach to stability of systems with time-varying delays. Automatica, 2011, 47: 235–238MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Boyd B, Ghoui L E, Feron E, et al. Linear matrix inequalities in system and control theory. SIAM, Philadelphia, 1994CrossRefGoogle Scholar
  42. 42.
    Liu J, Zhang J. Note on stability of discrete-time time varying delay system. IET Contr Theor Appl, 2012, 2: 335–339CrossRefGoogle Scholar
  43. 43.
    Wang J, Yang H. Exponential stability of a class of networked control systems with time delays and packet dropouts. Appl Math Comput, 2012, 218: 8887–8894MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Zhang L, Boukas E K, Shi P. Exponential H filtering for uncertain discrete-time switched linear systems with average dwell time: A µ-dependent approach. Int J Robust Nonlin, 2008, 18: 1188–1207MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Zhao Y, Gao H, Lam J, et al. Stability and stabilization of delayed TS fuzzy systems: a delay partitioning approach. IEEE T Fuzzy Syst, 2009, 17: 750–762CrossRefGoogle Scholar
  46. 46.
    Yue D, Tian E, Zhang Y, et al. Delay-distribution-dependent robust stability of uncertain systems with time-varying delay. Int J Robust Nonlin, 2009, 19: 377–393MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Mathiyalagan K, Su H, Shi P, et al. Exponential H filtering for discrete-time switched neural networks with random delays. IEEE T Cybern, 2015, 45: 676–687CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • JinDe Cao
    • 1
    Email author
  • R. Rakkiyappan
    • 2
  • K. Maheswari
    • 2
  • A. Chandrasekar
    • 2
  1. 1.Department of MathematicsSoutheast UniversityNanjingChina
  2. 2.Department of MathematicsBharathiar UniversityCoimbatoreIndia

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