Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 5147565, 9 pages
https://doi.org/10.1155/2018/5147565
Research Article

Improved Generalized Filtering for Static Neural Networks with Time-Varying Delay via Free-Matrix-Based Integral Inequality

Hui-Jun Yu,1,2 Yong He,3,4 and Min Wu3,4

1School of Information Science and Engineering, Central South University, Changsha, Hunan 410083, China
2School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China
3School of Automation, China University of Geosciences, Wuhan 430074, China
4Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan 430074, China

Correspondence should be addressed to Yong He

Received 18 July 2017; Revised 16 December 2017; Accepted 2 January 2018; Published 30 January 2018

Academic Editor: Renming Yang

Copyright © 2018 Hui-Jun Yu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. O. Chua and L. Yang, “Cellular Neural Networks: Applications,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 35, no. 10, pp. 1273–1290, 1988. View at Publisher · View at Google Scholar · View at Scopus
  2. X.-M. Zhang, Q.-L. Han, and X. Yu, “Survey on Recent Advances in Networked Control Systems,” IEEE Transactions on Industrial Informatics, vol. 12, no. 5, pp. 1740–1752, 2016. View at Publisher · View at Google Scholar · View at Scopus
  3. C.-K. Zhang, Y. He, L. Jiang, and M. Wu, “Stability analysis for delayed neural networks considering both conservativeness and complexity,” IEEE Transactions on Neural Networks and Learning Systems, vol. 27, no. 7, pp. 1486–1501, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. H.-B. Zeng, Y. He, P. Shi, M. Wu, and S.-P. Xiao, “Dissipativity analysis of neural networks with time-varying delays,” Neurocomputing, vol. 168, pp. 741–746, 2015. View at Publisher · View at Google Scholar · View at Scopus
  5. C.-K. Zhang, Y. He, L. Jiang, Q. H. Wu, and M. Wu, “Delay-dependent stability criteria for generalized neural networks with two delay components,” IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 7, pp. 1263–1276, 2014. View at Publisher · View at Google Scholar · View at Scopus
  6. Y. He, Q. G. Wang, and C. Lin, “An improved H8 filter design for systems with time-varying interval delay,” IEEE Trans. Circuits Syst. II, vol. 53, p. 1235, 2006. View at Google Scholar
  7. Y. He, G. P. Liu, D. Rees, and M. Wu, “Improved H∞ filtering for systems with a time-varying delay,” Circuits, Systems and Signal Processing, vol. 29, no. 3, pp. 377–389, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  8. H. Huang and G. Feng, “Delay-dependent H∞ and generalized H2 filtering for delayed neural networks,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 56, no. 4, pp. 846–857, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  9. C. K. Ahn and M. K. Song, “L2-L∞ filtering for time-delayed switched hopfield neural networks,” International Journal of Innovative Computing, Information and Control, vol. 7, no. 4, pp. 1831–1844, 2011. View at Google Scholar · View at Scopus
  10. D. Hu, H. Huang, and T. Huang, “Design of Arcak-type generalized H2 filter for delayed static neural networks,” Circuits, Systems and Signal Processing, vol. 33, no. 11, pp. 3635–3648, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  11. M. Hua, H. Tan, and J. Chen, “Delay-dependent H and generalized H2 filtering for stochastic neural networks with time-varying delay and noise disturbance,” Neural Computing and Applications, vol. 25, no. 3-4, pp. 613–624, 2014. View at Publisher · View at Google Scholar · View at Scopus
  12. Y. J. Li and Y. N. Liang, “Delay-dependent H∞ filtering for neural networks with time delay,” Applied Mechanics and Materials, vol. 511-512, pp. 875–879, 2014. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. He, G. P. Liu, D. Rees, and M. Wu, “Stability analysis for neural networks with time-varying interval delay,” IEEE Transactions on Neural Networks and Learning Systems, vol. 18, no. 6, pp. 1850–1854, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. Y. Li, J. Li, and M. Hua, “New results of H8 filtering for neural network with time-varying delay,” Int. J. Innov. Comput. Inf. Control, vol. 10, pp. 2309–2323, 2014. View at Google Scholar
  15. G. Liu, S. Zhou, X. Luo, and K. Zhang, “New filter design for static neural networks with mixed time-varying delays,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): Preface, vol. 9772, pp. 117–129, 2016. View at Publisher · View at Google Scholar · View at Scopus
  16. Y. Shu, X.-G. Liu, Y. Liu, and J. H. Park, “Improved Results on Guaranteed Generalized H2 Performance State Estimation for Delayed Static Neural Networks,” Circuits, Systems and Signal Processing, vol. 36, no. 8, pp. 3114–3142, 2017. View at Publisher · View at Google Scholar · View at Scopus
  17. H.-B. Zeng, Y. He, M. Wu, and J. She, “Free-matrix-based integral inequality for stability analysis of systems with time-varying delay,” Institute of Electrical and Electronics Engineers Transactions on Automatic Control, vol. 60, no. 10, pp. 2768–2772, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. C.-K. Zhang, Y. He, L. Jiang, M. Wu, and H.-B. Zeng, “Stability analysis of systems with time-varying delay via relaxed integral inequalities,” Systems & Control Letters, vol. 92, pp. 52–61, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  19. C.-K. Zhang, Y. He, L. Jiang, W.-J. Lin, and M. Wu, “Delay-dependent stability analysis of neural networks with time-varying delay: a generalized free-weighting-matrix approach,” Applied Mathematics and Computation, vol. 294, pp. 102–120, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. J. Sun, G. P. Liu, J. Chen, and D. Rees, “Improved delay-range-dependent stability criteria for linear systems with time-varying delays,” Automatica, vol. 46, no. 2, pp. 466–470, 2010. View at Publisher · View at Google Scholar · View at Scopus
  21. C. Ge, C. Hua, and X. Guan, “New delay-dependent stability criteria for neural networks with time-varying delay using delay-decomposition approach,” IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 7, pp. 1378–1383, 2014. View at Publisher · View at Google Scholar · View at Scopus
  22. C. Hua, S. Wu, X. Yang, and X. Guan, “Stability analysis of time-delay systems via free-matrix-based double integral inequality,” International Journal of Systems Science, vol. 48, no. 2, pp. 257–263, 2017. View at Publisher · View at Google Scholar · View at Scopus