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Mixed-delay-dependent L2-L Filtering for Neutral Stochastic Systems with Time-varying Delays

  • Yaobo Yu
  • Xiaoling Tang
  • Tao LiEmail author
  • Shumin Fei
Article
  • 24 Downloads

Abstract

This paper studies the issue on mixed-delay-dependent \(\mathcal{L}_2-\mathcal{L}_\infty\) filter design for a class of neutral stochastic system with time-varying delays. By making full use of the information and interrelationship of time-delays, an augmented Lyapunov-Krasovskii functional (LKF) is constructed for the filtering error system. In the derivation process, some Writinger-based integral inequalities and an extend reciprocal convex technique (ERCT) are utilized to estimate the lower bound of \(\mathcal{L}_2-\mathcal{L}_\infty\) disturbance attention level. Based on the derived stability criteria, two sufficient conditions on the existence of full-order \(\mathcal{L}_2-\mathcal{L}_\infty\) filter are presented in terms of linear matrix inequalities (LMIs), which can be easily tested and less conservative. Finally, two cases in an example are given to demonstrate the effectiveness of the proposed approach.

Keywords

\(\mathcal{L}_2-\mathcal{L}_\infty\) filter LMI approach mixed-delay-dependence neutral stochastic systems time-varying delay 

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References

  1. [1]
    W. Qian, L. Wang, and Z. Q. Chen. “Local consensus of nonlinear multi-agent systems with varying delay coupling,” IEEE Transections on Systems, Man, and Cybernetics: System, vol. 48, no. 12, pp. 2462–2469, 2018.CrossRefGoogle Scholar
  2. [2]
    W. Qian, Y. S. Cao, and Y Yang. “Global consensus of multi-agent systems with internal delays and communication delays.” IEEE Transations on Systems, Man, and Cybernetics: Systems, 2018. DOI: 10.1109/TSMC2018.2883108Google Scholar
  3. [3]
    C. Lien and J. Chen, “Discrete-delay-independent and discrete-delay-dependent criteria for a class of neutral systems,” ASME. J. Dyn. Sys., Meas., Control, vol. 125, no. 1, pp. 33–41, 2003.CrossRefGoogle Scholar
  4. [4]
    S. H. Long, Y. L. Wu, S. M. Zhong, and D. Zhang, “Stability analysis for a class of neutral type singular systems with time-varying delay,” Applied Mathematics and Computation, vol. 339, pp. 113–131, 2018.MathSciNetCrossRefGoogle Scholar
  5. [5]
    K. K. Ramakrishnan and G. G. Ray, “An improved delaydependent stability criterion for a class of lur’e systems of neutral type,” ASME. J. Dyn. Sys., Meas, Control, vol. 134, no. 1, pp. 011008-011008-6, 2011.Google Scholar
  6. [6]
    J. M. Park, S. Y. Lee, and P. G. Park, “An improved stability criteria for neutral-type Lur’e systems with time-varying delays,” Journal of the Franklin Institute, vol. 355, no. 12, pp. 5291–5309, 2018.MathSciNetCrossRefGoogle Scholar
  7. [7]
    L. Huang and X. Mao, “Delay-dependent exponential stability of neutral stochastic delay systems,” IEEE Transactions on Automatic Control, vol. 54, no. 1, pp. 147–152, 2009.MathSciNetCrossRefGoogle Scholar
  8. [8]
    B. Song, J. H. Park, Z. G. Wu, and Y. Zhang, “New results on delay-dependent stability analysis for neutral stochastic delay systems,” Journal of the Franklin Institute, vol. 350, no. 4, pp. 840–852, 2013.MathSciNetCrossRefGoogle Scholar
  9. [9]
    J. Wang, P. Hu, and H. Chen, “Delay-dependent exponential stability for neutral stochastic system with multiple time-varying delays,” IET Control Theory Applications, vol. 8, no. 17, pp. 2092–2101, 2014.MathSciNetCrossRefGoogle Scholar
  10. [10]
    U. Baszer, “Output feedback H control problem for linear neutral systems: delay independent case,” ASME. J. Dyn. Sys., Meas., Control, vol. 125, no. 2, pp. 177–185, 2003.CrossRefGoogle Scholar
  11. [11]
    Y. L. Dong, W. J. Liu, T. R. Li, and S. Liang, “Finite-time boundedness analysis and H control for switched neutral systems with mixed time-varying delays,” Journal of the Franklin Institute, vol. 354, no. 2, pp. 787–811, 2016.MathSciNetCrossRefGoogle Scholar
  12. [12]
    W. H. Chen, W. X. Zheng, and Y. Shen, “Delay-dependent stochastic stability and H control of uncertain neutral stochastic systems with time delay,” IEEE Transactions on Automatic Control, vol. 54, no. 7, pp. 1660–1667, 2009.MathSciNetCrossRefGoogle Scholar
  13. [13]
    M. S. Ali, K. Meenakshi, and H. Y. Joo, “Finite-time H filtering for discrete-time Markovian jump BAM neural networks with time-varying delays,” International Journal of Control, Automation, and Systems, vol. 16, no. 4, pp. 1971–1980, 2018.CrossRefGoogle Scholar
  14. [14]
    Y. Chen, A. Xue, and S. Zhou, “New delay-dependent \(\mathcal{L}_2-\mathcal{L}_\infty\) filter design for stochastic time-delay systems,” Signal Processing, vol. 89, no. 6, pp. 974–980, 2009.CrossRefGoogle Scholar
  15. [15]
    H. N. Wu, J. W. Wang, and P. Shi, “A delay decomposition approach to \(\mathcal{L}_2-\mathcal{L}_\infty\) filter design for stochastic systems with time-varying delay,” Automatica, vol. 47, no. 7, pp. 1482–1488, 2011.MathSciNetCrossRefGoogle Scholar
  16. [16]
    Y. Chen and W. X. Zheng, “\(\mathcal{L}_2-\mathcal{L}_\infty\) filtering for stochastic markovian jump delay systems with nonlinear perturbations,” Signal Processing, vol. 109, pp. 154–164, 2015.CrossRefGoogle Scholar
  17. [17]
    C. Gong, G. P. Zhu, and P. Shi, “\(\mathcal{L}_2-\mathcal{L}_\infty\) filtering for stochastic time-varying delay systems based on the Bessel-Legendre stochastic inequality,” Signal Processing, vol. 145, pp. 26–36, 2018.CrossRefGoogle Scholar
  18. [18]
    Z. J. Li, D. A. Zhao, and W. Xia, “\(\mathcal{L}_2-\mathcal{L}_\infty\) filter design for a class of neutral systems with interval time-varying delay,” Proc. of the Second International Conference on Computational Intelligence and Natural Computing (CINC), 2010.Google Scholar
  19. [19]
    L. Lin, H. Y. Wang, and S. D. Zhang, “\(\mathcal{L}_2-\mathcal{L}_\infty\) filter design for a class of neutral stochastic time delay systems,” Journal of the Franklin Institute, vol. 353, pp. 500–520, 2016.MathSciNetCrossRefGoogle Scholar
  20. [20]
    M. G. Hua, F. Q. Yao, P. Cheng, J. T. Fei, and J. J. Ni, “Delay-dependent \(\mathcal{L}_2-\mathcal{L}_\infty\) filtering for fuzzy neutral stochastic time-delay systems,” Signal Processing, vol. 137, pp. 98–108, 2017.CrossRefGoogle Scholar
  21. [21]
    G. B. Zhang, T. Wang, T. Li, and S. M. Fei, “Multiple integral lyapunov approach to mixed-delay-dependent stability of neutral neural networks,” Neurocomputing, vol. 275, no. 31, pp. 1782–1792, 2017.Google Scholar
  22. [22]
    M. J. Park, O. M. Kwon, J. H. Park, S. M. Lee, and E. J. Cha, “Stability of time-delay systems via wirtinger-based double integral inequality,” Automatica, vol. 55, pp. 204–208, 2015.MathSciNetCrossRefGoogle Scholar
  23. [23]
    C. K. Zhang, Y. He, L. Jiang, M. Wu, and Q. Wang, “An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay,” Automatica, vol. 85, pp. 481–485, 2017.MathSciNetCrossRefGoogle Scholar
  24. [24]
    T. Li, A. G. Song, S. M. Fei, and T. Wang, “Delayderivative-dependent stability for delayed neural networks with unbound distributed delay,” IEEE Transactions on Neural Networks, vol. 21, no. 8, pp. 1365–1371, 2010.CrossRefGoogle Scholar
  25. [25]
    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-weightingmatrix approach,” Applied Mathematics and Computation, vol. 294, pp. 102–120, 2017.MathSciNetCrossRefGoogle Scholar
  26. [26]
    F. Long, C. K. Zhang, Y. He, L. Jiang, Q. G. Wang, and M. Wu, “Stability analysis of Lur’e systems with additive delay components via a relaxed matrix inequality,” Applied Mathematics and Computation, vol. 328, pp. 224–242, 2018.MathSciNetCrossRefGoogle Scholar
  27. [27]
    D. Higham, “An algorithmic Introduction to numerical simulation of stochastic differential equations,” SIAM Rev, vol. 43, pp. 525–546, 2001.MathSciNetCrossRefGoogle Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.School of Automation EngineeringNanjing University of Aeronautics and AstronauticsNanjingP. R. China
  2. 2.School of AutomationSoutheast UniversityNanjingP. R. China

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