Advertisement

A New Global Robust Exponential Stability Criterion for H Control of Uncertain Stochastic Neutral-type Neural Networks with Both Timevarying Delays

  • Maharajan Chinnamuniyandi
  • Raja Ramachandran
  • Jinde Cao
  • Grienggrai Rajchakit
  • Xiaodi Li
Regular Paper Control Theory and Applications
  • 57 Downloads

Abstract

This paper mainly focuses on a novel H control design to handle the global robust exponential stability problem for uncertain stochastic neutral-type neural networks (USNNNs) with mixed time-varying delays. Here the delays are assumed to be both discrete and distributed, which means that the lower and upper bounds can be derived. Firstly, we draw a control law for stabilized and stability of the neutral-type neural networks (NNNs). Secondly, by employing the Lyapunov-Krasovskii functional(LKF) theory, Jensen’s integral inequality, new required sufficient conditions for the global robust exponential stability of the given neural networks (NNs) are established in terms of delay-dependent linear matrix inequalities (LMIs), which can be easily checked in practice. The conditions obtained are expressed in terms of LMIs whose feasibility can be verified easily by MATLAB LMI control toolbox. Moreover, we have compared our work with previous one in the existing literature and showed that it reduces conservatism. Finally, one numerical example with their simulations is given to validate the effectiveness of our proposed theoretical results.

Keywords

Global robust exponential stability H control Linear matrix inequality Lyapunov-Krasovskii functional Mixed time-varying delays Stochastic uncertain neutral-type neural networks 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. Sakthivel, R. Anbuvithya, K. Mathiyalagan, Y. K. Ma, and P. Prakash, “Reliable anti-synchronization conditions for BAM memristive neural networks with different memductance functions,” Applied Mathematics and Computation, vol. 275, pp. 213–228, 2016.MathSciNetCrossRefGoogle Scholar
  2. [2]
    R. Sakthivel, M. Sathishkumar, B. Kaviarasan, and S. M. Anthoni, “Robust finite-time passivity for discrete-time genetic regulatory networks with Markovian jumping parameters,” Zeitschrift Naturforschung A, vol. 71, no. 4, pp. 289–304, 2016. [click]Google Scholar
  3. [3]
    X. Li and J. Wu, “Stability of nonlinear differential systems with state-dependent delayed impulses,” Automatica, vol. 64, pp. 63–69, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    X. Zhang, G. Lu, and Y. Zheng, “Synchronization for timedelay Lur’e systems with sector and slope restricted nonlinearities under communication constraints,” Circuits, Systems, and Signal Processing, vol. 30, no. 6, pp. 1573–1593, 2011. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    M. Syed Ali, N. Gunasekaran, and Q. Zhu, “State estimation of fuzzy delayed neural networks with Markovian jumping parameters using sampled-data control,” Fuzzy Sets and Systems, vol. 306, pp. 87–104, 2017. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    J. Cao, D. Huang, and Y. Qu, “Global robust stability of delayed recurrent neural networks,” Chaos Solitons & Fractals, vol. 23, pp. 221–229, 2005.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    X. Li and J. Cao, “An impulsive delay inequality involving unbounded time-varying delay and applications,” IEEE Transactions on Automatic Control, vol. 62, pp. 3618–3625, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    M. Syed Ali, P. Balasubramaniam, and Q. Zhu, “Stability of stochastic fuzzy BAM neural networks with discrete and distributed time-varying delays,” International Journal of Machine Learning and Cybernetics, vol. 8, no. 1, pp. 263–273, 2017. [click]CrossRefGoogle Scholar
  9. [9]
    X. Li and J. Cao, “Delay-dependent stability of neural networks of neutral type with time delay in the leakage term,” Nonlinearity, vol. 23, no. 7, 2010.Google Scholar
  10. [10]
    R. Saravanakumar, M. Syed Ali, J. Cao, and H. Huang, “H state estimation of generalised neural networks with interval time-varying delays,” International Journal of Systems Science, vol. 47, no. 16, pp. 3888–3899, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    X. Mao, X. Li, and J. Liu, “New robust stability criterion for neural networks of neutral type with time-varying delays,” Fourth International Conference on Natural Computation, 2008.Google Scholar
  12. [12]
    R. Rakkiyappan, Q. Zhu, and A. Chandrasekar, “Stability of stochastic neural networks of neutral type with Markovian jumping parameters: A delay-fractioning approach,” Journal of the Franklin Institute, vol. 351, no. 3, pp. 1553–1570, 2014.MathSciNetCrossRefGoogle Scholar
  13. [13]
    B. Lee and J. Lee, “Robust stability and stabilization of linear delayed systems with structured uncertainty,” Automatica, vol. 35, no. 6, pp. 1149–1154, 1999. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    L. H. Xie, “Output feedback H control of systems with parameter uncertainty,” Int. J. Control, vol. 63, pp. 741–750, 1996.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    R. Li and J. Cao, “Dissipativity analysis of memristive neural networks with time-varying delays and randomly occurring uncertainties,” Mathematical Methods in the Applied Sciences, vol. 39, no. 11, pp. 2896–2915, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    W. Xie and Q. Zhu, “Mean square exponential stability of stochastic fuzzy delayed Cohen rossberg neural networks with expectations in the coefficients,” Neurocomputing, vol. 166, pp. 133–139, 2015. [click]CrossRefGoogle Scholar
  17. [17]
    H. Zhang, M. Dong, Y. Wang, and N. Sun, “Stochastic stability analysis of neutral-type impulsive neural networks with mixed time-varying delays and Markovian jumping,” Neurocomputing, vol. 73, pp. 2689–2695, 2010.CrossRefGoogle Scholar
  18. [18]
    F. Yao, J. Cao, P. Cheng, and L. Qiu, “Generalized average dwell time approach to stability and input-to-state stability of hybrid impulsive stochastic differential systems,” Nonlinear Analysis: Hybrid Systems, vol. 22, pp. 147–160, 2016.MathSciNetzbMATHGoogle Scholar
  19. [19]
    L. Liu and Q. Zhu, “Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks,” Applied Mathematics and Computation, vol. 266, pp. 698–712, 2015. [click]MathSciNetCrossRefGoogle Scholar
  20. [20]
    X. Xiao, L. Zhou, D. Ho, and G. Lu, “Conditions for stability of linear continuous Markovian switching singular systems,” IET Control Theory & Applications, vol. 8, no. 3, pp. 168–174, 2014.MathSciNetCrossRefGoogle Scholar
  21. [21]
    Y. Wu, Y. Wu, and Y. Chen, “Mean square exponential stability of uncertain stochastic neural networks with timevarying delay,” Neurocomputing, vol. 72, pp. 2379–2384, 2009.CrossRefGoogle Scholar
  22. [22]
    G. Zames, “Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms and approximate inverses,” IEEE Transactions on automatic control, vol. 26, no. 2, pp. 301–320, 1981. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    Y. Du, X. Li, and S. Zhong, “Robust reliable H control for neural networks with mixed time delays,” Chaos, Solitons and Fractals, vol. 91, pp. 1–9, 2016.MathSciNetCrossRefGoogle Scholar
  24. [24]
    M. Ali and R. Saravanakumar, “Improved delay-dependent robust H control of an uncertain stochastic system with interval time-varying and distributed delays,” Chinese Physics B, vol. 23, no. 12, pp. 209–231, 2014. [click]Google Scholar
  25. [25]
    S. Lakshmanan, K. Mathiyalagan, J. H. Park, R. Sakthivel, and F. A. Rihan, “Delay-dependent H state estimation of neural networks with mixed time-varying delays,” Neurocomputing, vol. 129, pp. 392–400, 2014.CrossRefGoogle Scholar
  26. [26]
    K. Mathiyalagan, R. Anbuvithya, R. Sakthivel, J. H. Park, and P. Prakash, “Non-fragile H synchronization of memristor-based neural networks using passivity theory,” Neural Networks, vol. 74, pp. 85–100, 2016. [click]CrossRefGoogle Scholar
  27. [27]
    R. Saravanakumar, M. S. Ali, and M. Hua, “H state estimation of stochastic neural networks with mixed timevarying delays,” Soft Computing, vol. 20, no. 9, pp. 3475–3487, 2016.CrossRefzbMATHGoogle Scholar
  28. [28]
    I. Stamova, T. Stamov, and X. Li, “Global exponential stability of a class of impulsive cellular neural networks with Supremums,” International Journal of Adaptive Control and Signal Processing, vol. 28, pp. 1227–1239, 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    E. Boukas and Z. Lin, Deterministic and Stochastic Time Delay Systems, Birkhauser, Boston, vol. 187, 2002.Google Scholar
  30. [30]
    J. Park, “An analysis of global robust stability of uncertain cellular neural networks with discrete and distributed delays,” Chaos, Solitons & Fractals, vol. 32, no. 2, pp. 800–807, 2007.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    M. Syed Ali, S. Arik, and R. Saravanakumar, “Delaydependent stability criteria of uncertain Markovian jump neural networks with discrete interval and distributed timevarying delays,” Neurocomputing, vol. 158, pp. 167–173, 2015. [click]CrossRefGoogle Scholar
  32. [32]
    X. Li, M. Bohner, and C. Wang, “Impulsive differential equations: Periodic solutions and applications,” Automatica vol.52, pp. 173–178, 2015.Google Scholar
  33. [33]
    Q. Zhou, X. Shao, J. Zhu, and H. Karimi, “Stability analysis for uncertain neural networks of neutral type with timevarying delay in the leakage term and distributed delay,” Abstract and Applied Analysis, vol. 2013, pp. 4339–4344, 2013.zbMATHGoogle Scholar
  34. [34]
    Y. Fang, K. Li, and Y. Yan, “Novel robust exponential stability of Markovian jumping impulsive delayed neural networks of neutral-type with stochastic perturbation,” Mathematical Problems in Engineering, Article, vol. 3, pp. 1–20, 2016.Google Scholar
  35. [35]
    P. Balasubramaniam, G. Nagamani, and R. Rakkiyappan, “Global passivity analysis of interval neural networks with discrete and distributed delays of neutral type,” Neural Processing Letters, vol. 32, pp. 109–130, 2013.CrossRefGoogle Scholar
  36. [36]
    C. Y. Lu, “A delay-dependent approach to robust control for neutral uncertain neural networks with mixed interval time-varying delays,” Nonlinearity, vol. 24, pp. 1121–1136, 2011.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Maharajan Chinnamuniyandi
    • 1
  • Raja Ramachandran
    • 2
  • Jinde Cao
    • 3
    • 4
  • Grienggrai Rajchakit
    • 5
  • Xiaodi Li
    • 6
  1. 1.Department of MathematicsAlagappa UniversityKaraikudiIndia
  2. 2.Ramanujan Centre for Higher MathematicsAlagappa UniversityKaraikudiIndia
  3. 3.School of MathematicsSoutheast UniversityNanjingChina
  4. 4.School of Electrical EngineeringNantong UniversityNantongChina
  5. 5.Department of Mathematics, Faculty of ScienceMaejo UniversityChiang MaiThailand
  6. 6.School of Mathematics and StatisticsShandong Normal UniversityJi’nanP. R. China

Personalised recommendations