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New Delay-dependent stability criteria for neutral systems with time-varying delay using delay-decomposition approach

  • Control Theory
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Abstract

This paper concerns with the problem of asymptotic stability for neutral systems with timevarying delays. With the introduction of delay-decomposition approach, some new delay-dependent stability criteria are established and formulated in the form of linear matrix inequalities. Both constant time delays and time-varying delays have been taken into account. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

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References

  1. H. R. Karimi, M. Zapateiro, and N. Luo, “Stability analysis and control synthesis of neutral systems with time-varying delays and nonlinear uncertainties,” Chaos, Solitons and Fractals, vol. 42, no. 1, pp. 595–603, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  2. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press Boston, 1993.

    MATH  Google Scholar 

  3. R. K. Brayton, “Bifurcation of periodic solutions in a nonlinear difference-differential equation of neutral type,” Quarterly of Applied Mathematics, vol. 24, pp. 215–224, 1966.

    MATH  MathSciNet  Google Scholar 

  4. S. I. Niculescu, Delay Effects on Stability: A Robust ai]Control Approach, Springer Berlin, 2001.

    Google Scholar 

  5. O. M. Kwon, J. H. Park, and S. M. Lee, “On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays,” Applied Mathematics and Computation, vol. 197, no. 2, pp. 864–873, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  6. G. D. Hu, “Some simple stability criteria of neutral delay-differential systems,” Applied Mathematics and Computation, vol. 80, no. 2, pp. 257–271, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. S. Mahmoud, “Robust H8 control of linear neutral systems,” Automatica, vol. 36, no. 5, pp. 757–764, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  8. J. D. Chen, C. H. Lien, K. K. Fan, and J. S. Cheng, “Delay-dependent stability criterion for neutral time-delay systems,” Electronics Letters, vol. 36, no. 22, pp. 1897–1898, 2000.

    Article  Google Scholar 

  9. M. J. Park, O. M. Kwon, J. H. Park, and S. M. Lee, “Delay-dependent stability criteria for linear timedelay system of neutral type,” World Academy Science and Engineering Technology, vol. 70, pp. 1014–1018, 2010.

    Google Scholar 

  10. P. G. Park, “A delay-dependent stability criterion for systems with uncertain time-invariant delays,” IEEE Trans. Autom. Control, vol. 44, no. 4, pp. 876–877, 1999.

    Article  MATH  Google Scholar 

  11. M. Wu, Y. He, J. H. She, and G. P. Liu, “Delay dependent criteria for robust stability of timevarying delay systems,” Automatica, vol. 40, no. 8, pp. 1435–1439, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  12. O. M. Kwon and J. H. Park, “On improved delaydependent robust control for uncertain time-delay systems,” IEEE Trans. Autom. Control, vol. 49, no. 11, pp. 1991–1995, 2004.

    Article  MathSciNet  Google Scholar 

  13. K. Gu, “Discretized Lyapunov functional for uncertain systems with multiple time-delay,” International Journal of Control, vol. 72, no. 16, pp. 1436–1445, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  14. O. M. Kwon, J. H. Park, and S. M. Lee, “An improved delay-dependent criterion for asymptotic stability of uncertain dynamic systems with timevarying delays,” Journal of Optimization Theory and Applications, vol. 145, no. 2, pp. 343–353, 2010.

    Article  MATH  MathSciNet  Google Scholar 

  15. O. M. Kwon, M. J. Park, J. H. Park, S. M. Lee, and E. J. Cha, “New delay-partitioning approaches to stability criteria for uncertain neutral systems with time-varying delays,” Journal of the Franklin Institute, vol. 349, no. 9, pp. 2799–2823, 2012.

    Article  MATH  MathSciNet  Google Scholar 

  16. H. Huang and G. Feng, “State estimation of recurrent neural networks with time-varying delay: A novel delay partition approach,” Neurocomputing, vol. 74, no. 5, pp.792–796, 2011.

    Google Scholar 

  17. S. Zhu, Z. Li, and C. Zhang, “Delay decomposition approach to delay-dependent stability for singular time-delay systems,” IET Control Theory Applications, vol. 4, no. 11, pp. 2613–2620, 2010.

    Article  MathSciNet  Google Scholar 

  18. P. L. Liu, “A delay decomposition approach to robust stability analysis of uncertain systems with time-varying delay,” ISA transactions, vol. 51, no. 6, pp. 694–701, 2012.

    Article  Google Scholar 

  19. P. L. Liu, “Further results on the stability analysis of singular systems with time-varying delay: a delay decomposition approach,” International Journal of Analysis, ID 721407, 1–11, 2013.

    Article  Google Scholar 

  20. X. M. Zhang and Q. L. Han, “New Lyapunov-Krasovskii functionals for global asymptotic stability of delayed neural networks,” IEEE Trans. ai]Neural Netw., vol. 20, no. 3, pp. 533–539, 2009.

    Article  Google Scholar 

  21. P. G. Park, J. W. Ko, and C. Jeong, “Reciprocally convex approach to stability of systems with timevarying delays,” Automatica, vol. 47, no. 1, pp. 235–238, 2011.

    Article  MATH  MathSciNet  Google Scholar 

  22. S. H. Kim, P. G. Park, and C. Jeong, “Robust H8 stabilization of networked control systems with packet analyser,” IET Control Theory and Applications, vol. 4, no. 1, pp. 1828–1837, 2010.

    Article  Google Scholar 

  23. P. Balasubramaniam, R. Krishnasamy, and R. Rakkiyappan, “Delay-dependent stability of neutral systems with time-varying delays using delay decomposition approach,” Applied Mathematical Modelling, vol. 36, no. 5, pp. 2253–2261, 2012.

    Article  MATH  MathSciNet  Google Scholar 

  24. Y. He, Q. G. Wang, C. Lin, and M. Wu, “Delayrange-dependent stability for systems with timevarying delay,” Automatica, vol. 43, no. 2, pp. 371–376, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  25. P. G. Park and J. W. Ko, “Stability and robust stability for systems with a time-varying delay,” Automatica, vol. 43, no. 10, pp. 1855–1858, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  26. J. W. Ko and P. G. Park, “Delay-dependent stability criteria for systems with asymmetric bounds on delay derivative,” Journal of the Franklin Institute, vol. 348, no. 9, pp. 2674–2688, 2011.

    Article  MATH  MathSciNet  Google Scholar 

  27. M. N. A. Parlakci, “Robust stability of uncertain neutral systems: a novel augmented Lyapunov functional approach,” IET Control Theory and Applications, vol. 1, no. 3, pp. 802–809, 2007.

    Article  MathSciNet  Google Scholar 

  28. J. Sun, G. P. Liu, and J. Chen, “Delay-dependent stability and stabilization of neutral time-delay systems,” International Journal of Robust and Nonlinear Control, vol. 19, no. 12, pp. 1364–1375, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  29. X. Nian, H. Pang, W. Gui, and H. Wang, “New stability analysis for linear neutral system via state matrix decomposition,” Applied Mathematics and Computation, vol. 215, no. 5, pp. 1830–1837, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  30. M. J. Park, O. M. Kwon, J. H. Park, and S. M. Lee, “A new augmented Lyapunov-Krasovskii functional approach for stability of linear systems with time-varying delays,” Applied Mathematics and Computation, vol. 217. no. 17, pp. 7197–7209, 2011.

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Chang-Chun Hua.

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Ge, C., Hua, CC. & Guan, XP. New Delay-dependent stability criteria for neutral systems with time-varying delay using delay-decomposition approach. Int. J. Control Autom. Syst. 12, 786–793 (2014). https://doi.org/10.1007/s12555-013-0118-5

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  • DOI: https://doi.org/10.1007/s12555-013-0118-5

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