Advertisement

An Improved Result on \(H_{\infty }\) Performance State Estimation of Delayed Static Neural Networks

  • Guoqiang Tan
  • Jidong Wang
  • Zhanshan WangEmail author
  • Xiaolong Qian
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11554)

Abstract

In this paper, a new state estimator with integral term is proposed for studying the \(H_{\infty }\) performance of static neural networks with time-varying delay. Firstly, some integral inequalities are given to handle the derivative of Lyapunov functional. Secondly, a delay dependent criterion is derived for the estimation error system. Thirdly, in order to guarantee the \(H_{\infty }\) performance, the gain matrices can be obtained by the linear matrix inequalities. Finally, an example is used to verify the effectiveness of our proposed method.

Keywords

\(H_{\infty }\) performance Time-varying delay Static neural networks Linear matrix inequalities. 

Notes

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61473070, 61433004, 61627809), and in part by SAPI Fundamental Research Funds (Grant No. 2018ZCX22).

References

  1. 1.
    Liu, H., Wang, Z., Shen, B., Liu, X.: Event-triggered \(H_{\infty }\) state estimation for delayed stochastic memristive neural networks with missing measurements: the discrete time case. IEEE Trans. Neural Netw. Learn. Syst. 29, 3726–3737 (2018)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Duan, Q., Su, H., Wu, Z.G.: \(H_{\infty }\) state estimation of static neural networks with time-varying delay. Neurocomputing 97, 16–21 (2012)CrossRefGoogle Scholar
  3. 3.
    Zhang, X.-M., Han, Q.-L.: Global asymptotic stability for a class of generalized neural networks with interval time-varying delay. IEEE Trans. Neural Netw. 22, 1180–1192 (2011)CrossRefGoogle Scholar
  4. 4.
    Qiao, H., Peng, J., Xu, Z.-B., Zhang, B.: A reference model approach to stability analysis of neural networks. IEEE Trans. Syst. Man Cybern. B Cybern. 33, 925–936 (2003)CrossRefGoogle Scholar
  5. 5.
    Huang, H., Feng, G., Cao, J.: Guaranteed performance state estimation of static neural networks with time-varying delay. Neurocomputing 74, 606–616 (2011)CrossRefGoogle Scholar
  6. 6.
    Zhang, H., Wang, Z., Liu, D.: A comprehensive review of stability analysis of continuous-time recurrent neural networks. IEEE Trans. Neural Netw. Learn. Syst. 25, 1229–1262 (2014)CrossRefGoogle Scholar
  7. 7.
    Zhang, X.-M., Han, Q.-L.: Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach. Neural Netw. 54, 57–69 (2014)CrossRefGoogle Scholar
  8. 8.
    Zhang, C.K., He, Y., Jiang, L., Wu, M.: Stability analysis for delayed neural networks considering both conservativeness and complexity. IEEE Trans. Neural Netw. Learn. Syst. 27, 1486–1501 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Wang, Z., Ho, D.W.C., Liu, X.: State estimation for delayed neural networks. IEEE Trans. Neural Netw. 16, 279–284 (2005)CrossRefGoogle Scholar
  10. 10.
    Yao, Y.X., Radun, A.V.: Proportional integral observer design for linear systems with time delay. IET Control Theory Appl. 1, 887–892 (2007)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Liu, B., Ma, X., Jia, X.-C.: Further results on \(H_{\infty }\) state estimation of static neural networks with time-varying delay. Neurocomputing 285, 133–140 (2018)CrossRefGoogle Scholar
  12. 12.
    Zhang, X.-M., Han, Q.-L., Wang, Z.-D., Zhang, B.-L.: Neural state estimation for neural networks with two additive time-varying delay components. IEEE Trans. Cybern. 47, 3184–3194 (2017)CrossRefGoogle Scholar
  13. 13.
    Huang, H., Huang, T., Chen, X.: Guaranteed \(H_{\infty }\) performance state estimation of delayed static neural networks. IEEE Trans. Circ. Syst. II Exp. Briefs. 60, 371–375 (2013)Google Scholar
  14. 14.
    Huang, H., Huang, T., Chen, X.: Further result on guranteed \(H_{\infty }\) performance state estimation of delayed static neural networks. IEEE Trans. Neural Netw. Learn. Syst. 26, 1335–1341 (2015)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Zhang, X.M., Han, Q.L.: State estimation for static neural networks with time-varying delays based on an improved reciprocally convex inequality. IEEE Trans. Neural Netw. Learn. Syst. 29, 1376–1381 (2018)CrossRefGoogle Scholar
  16. 16.
    He, Y., Wang, Q.-G., Wu, M., Lin, C.: Delay-dependent state estimation for delayed neural networks. IEEE Trans. Neural Netw. 17, 1077–1081 (2006)CrossRefGoogle Scholar
  17. 17.
    Park, P.G., Ko, J.W., Jeong, C.: Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47, 235–238 (2011)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Zemouche, A., Boutayeb, M.: Comments on “a note on observers for discrete-time Lipschitz nonlinear systems”. IEEE Trans. Circ. Syst. II Exp. Briefs. 60, 56–60 (2013)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Guoqiang Tan
    • 1
  • Jidong Wang
    • 1
    • 2
  • Zhanshan Wang
    • 1
    Email author
  • Xiaolong Qian
    • 1
  1. 1.School of Information Science and EngineeringNortheastern UniversityShenyangChina
  2. 2.School of Electrical EngineeringNorth China University of Water Resources and Electric PowerZhengzhouChina

Personalised recommendations