Advertisement

Robust H Performance of Discrete-time Neural Networks with Uncertainty and Time-varying Delay

  • M. Syed Ali
  • K. Meenakshi
  • R. Vadivel
  • O. M. Kwon
Regular Papers Control Theory and Applications
  • 36 Downloads

Abstract

In this paper, we are concerned with the robust H problem for a class of discrete-time neural networks with uncertainties. Under a weak assumption on the activation functional, some novel summation inequality techniques and using a new Lyapunov-Krasovskii (L-K) functional, a delay-dependent condition guaranteeing the robust asymptotically stability of the concerned neural networks is obtained in terms of a Linear Matrix Inequality(LMI). It is shown that this stability condition is less conservative than some previous ones in the literature. The controller gains can be derived by solving a set of LMIs. Finally, two numerical examples result are given to illustrate the effectiveness of the developed theoretical results.

Keywords

H control linear matrix inequality stability time-varying delay 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. Sakthivel, K. Mathiyalagan, and S. Marshal Anthoni, “Robust H control for uncertain discrete-time stochastic neural networks with time-varying delays,” IET Control Theory Appl., vol. 6, pp. 1220–1228, July 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    A. Arunkumar, R. Sakthivel, K. Mathiyalagan, and S. Marshal Anthoni, “Robust stability criteria for discrete-time switched neural networks with various activation functions,” Appl. Math. Comput., vol. 218, pp. 10803–10816, July 2012.MathSciNetzbMATHGoogle Scholar
  3. [3]
    L. J. Banu, P. Balasubramaniam, and K. Ratnavel, “Robust stability analysis for discrete-time uncertain neural networks with leakage time-varying delay,” Neurocomputing, vol. 151, pp. 808–816, March 2015.CrossRefGoogle Scholar
  4. [4]
    X. G. Liu, F. X. Wang, and Y. J. Shu, “A novel summation inequality for stability analysis of discrete-time neural networks,” J. Comput. Appl. Math., vol. 304, pp. 160–171, October 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    L. Jin, Y. Hen, and W. Wu, “Improved delay-dependent stability analysis of discrete-time neural networks with time-varying delay,” J. Franklin Inst., vol. 354, no. 4, pp. 1922–1936, March 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    M. Luo, S. Zhong, R. Wang, and W. Kang, “Robust stability analysis for discrete-time stochastic neural networks systems with time-varying delays,” Appl. Math. Comput., vol.209, no. 2, pp. 305–313, March 2009.MathSciNetzbMATHGoogle Scholar
  7. [7]
    T. Zhang, “Comment on delay-dependent robust H filtering for uncertain discrete-time singular systems with interval time-varying delay,” Automatica, vol. 53, pp. 291–292, March 2015.CrossRefzbMATHGoogle Scholar
  8. [8]
    D. Liu, L. Wang, Y. Pan, and H. Ma, “Mean square exponential stability for discrete-time stochastic fuzzy neural networks with mixed time-varying delay,” Neurocomputing, vol. 171, pp. 1622–1628, January 2016.CrossRefGoogle Scholar
  9. [9]
    J. Chen, I.T. Wu, and C.H. Lien, “Robust exponential stability for uncertain discrete-time switched systems with interval time-varying delay through a switching signal,” J. Appl. Rrh. Technol., vol. 12, no. 6, pp. 1187–1197, December 2014.CrossRefGoogle Scholar
  10. [10]
    Y. Shan, S. Zhong, J. Cui, L. Hou, and Y. Li, “Improved criteria of delay-dependent stability for discrete-time neural networks with leakage delay,” Neurocomputing, vol. 226, pp. 409–419, November 2017.CrossRefGoogle Scholar
  11. [11]
    K. Ramakrishnan and G. Ray, “Robust stability criteria for a class of uncertain discrete-time systems with time-varying delay,” Appl. Math. Model., vol. 37 no. 3, pp. 1468–1479, February 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    B. Yeon and H. Ahn, “Stability analysis of spatiall inter-connected discrete-time systems with random delays and structured uncertainties,” J. Franklin Inst., vol. 350, no. 7, pp. 1719–1738, September 2013.MathSciNetCrossRefGoogle Scholar
  13. [13]
    G. Chesi and R. H. Middleton, “Robust stability and performance analysis of 2D mixed continuous-discrete-time systems with uncertainty,” Automatica, vol. 67, pp. 233–243, May 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    L. J. Banu and P. Balasubramaniam, “Admissibility analysis for discrete-time singular systems with randomly occurring uncertainties via delay-divisioning approach,” ISA Trans., vol. 59, pp. 354–362, November 2015.CrossRefGoogle Scholar
  15. [15]
    L. Jarina Banu, and P. Balasubramaniam, “Robust stability analysis for discrete-time neural networks with timevarying leakage delays and random parameter uncertainties,” Neurocomputing, vol. 179, no. 29, pp. 134–126, February 2016.Google Scholar
  16. [16]
    Y. Li and G. H. Yang, “Robust adaptive fuzzy control of a class of uncertain switched nonlinear systems with mismatched uncertainties,” Inf. Sci., vol. 339, no. 20, pp. 290–309, April 2016.CrossRefGoogle Scholar
  17. [17]
    M. Hashemi, J. Askari, and J. Ghaisar, “Adaptive decentralised dynamic surface control for non-linear large-scale systems against actuator failures,” IET Control Theory Appl. vol. 10, no. 1, pp. 44–57, January 2016.MathSciNetCrossRefGoogle Scholar
  18. [18]
    H. Liu, Y. Pan, S. Li, and Y. Chen, “Adaptive fuzzy backstepping control of fractional-order nonlinear systems,” IEEE Trans. Systems, Man Cybern. Syst. vol. 47 no.8 pp. 2209–2217 August 2017.CrossRefGoogle Scholar
  19. [19]
    Y. Pan and H. Yu, “Composite learning from adaptive dynamic surface control,” IEEE Transa. Automat. Cont. vol. 61 no. 9 pp. 2603–2609 September 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    H. Liu, Y. Pan, S. Li, and Y. Chen, “Synchronization for fractional-order neural networks with full/under-actuation using fractional-order sliding mode control,” Int. J. Mach. Learn. & Cyber., 2017.Google Scholar
  21. [21]
    T. Fujinami, Y. Saito, M. Morishita, Y. Koike, and K. Tanida, “A hybrid mass damper system controlled by H control theory for reducing bending-torsion vibration of an actual building,” Earthq. Eng. Struct. Dyn. vol. 30, pp. 1639–1653, 2001.CrossRefGoogle Scholar
  22. [22]
    C. Hu, K. Yu, and L. Wu, “Robust H switching control and switching signal design for uncertain discrete switched systems with interval time-varying delay,” J. Franklin Inst., vol. 351, no. 1, pp. 565–578, January 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    Y. Li and J. Qi, “Robust H control of uncertain stochastic time-delay linear repetitive processes,” J. Control Theory Appl., vol. 8, no. 4, pp. 491–495, November 2010.MathSciNetCrossRefGoogle Scholar
  24. [24]
    M. Abbaszadeh and H. J. Marquez, “Nonlinear robust H filtering for a class of uncertain systems via convex optimization,” J. Control Theory Appl., vol. 10, no. 2, pp. 152–158, May 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    L. K. Wang and X. D. Liu, “Robust H fuzzy control for discrete-time nonlinear systems,” Int. J. Control Autom. Syst., vol. 8, no. 1, pp. 118–126, February 2010.MathSciNetCrossRefGoogle Scholar
  26. [26]
    D. Wang, W. Wang, and P. Shi, “Design on H -filtering for discrete-time switched delay systems,” Int. J. Syst. Sci., vol. 42, no. 12, pp. 1965–1973, December 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    S. Chae, D. Huang, and S. K. Nguang, “Robust partially mode delay dependent H control of discrete-time networked control systems,” Int. J. Syst. Sci., vol. 43, pp. 1764–1773, February 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    Q. Song and Z. Wang, “A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays,” Phys. Lett. A, vol. 368, pp. 134–145, August 2007.CrossRefGoogle Scholar
  29. [29]
    B. Zhang, S. Xu, and Y. Zou, “Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with timevarying delays,” Neurocomputing, vol. 72, no. 1–3, pp. 321–330, December 2008.CrossRefGoogle Scholar
  30. [30]
    J. Yu, K. Zhang, and S. Fei, “Exponential stability criteria for discrete-time recurrent neural networks with timevarying delay,” Nonlinear Anal. Real World Appl., vol. 11, no. 1, pp. 207–216, February 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    S. Ramasamy, G. Nagamani, and Radhika, “Further results on dissipativity criterion for Markovian jump discrete-time neural networks with two delay components via discrete wirtinger inequality approach,” Neural Process. Lett., vol. 45, no. 3, pp. 939–965, June 2017.CrossRefGoogle Scholar
  32. [32]
    R. Saravanakumar, G. Rajchakit, M. Syed Ali, Z. Xiang and Y. Hoon Joo, “Robust extended dissipativity criteria for discrete-time uncertain neural networks with time-varying delays,” Neural Comput & Applic., May 2017.Google Scholar
  33. [33]
    C. K. Zhang, Y. He, L. Jiang, Q. Wang, and M. Wu, “Stability analysis of discrete-time neural networks with time-varying delay via an extended reciprocally convex matrix inequality,” IEEE Trans. Cybern., vol. 47, no. 10, pp. 3040–3049, February 2017.CrossRefGoogle 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

  • M. Syed Ali
    • 1
  • K. Meenakshi
    • 1
  • R. Vadivel
    • 1
  • O. M. Kwon
    • 2
  1. 1.Department of MathematicsThiruvalluvar UniversityVelloreIndia
  2. 2.School of Electrical EngineeringChungbuk National UniversityCheongjuKorea

Personalised recommendations