Skip to main content
SpringerLink
Log in

Delay-Derivative-Dependent Stability for Neutral Systems with Time-Varying Delay and Nonlinearity

  • Research Article - Systems Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

The asymptotical stability for a class of neutral systems with time-varying delay and restricted nonlinearity is investigated. Firstly, during choosing the Lyapunov–Krasovskii functional (LKF), two adjusting scalars \(\alpha ,\beta \in (0,1]\) will be introduced and they can effectively reduce the conservatism once the upper bound of delay derivative is very large. Then by utilizing some integral inequalities, the much tighter bound on LKF derivative is presented and some previously ignored information can be fully utilized by employing an extended convex combination technique. Furthermore, two stability criteria are presented in terms of LMIs and they can be easily checked. Finally, some numerical examples with comparing results can illustrate the superiorities of the derived results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Samli, R.; Arik, S.: New results for global stability of a class of neutral-type neural systems with time delays. Appl. Math. Comput. 210(2), 564–570 (2009)

    MathSciNet  MATH  Google Scholar 

  2. Park, J.H.; Kwon, O.: On new stability criterion for delay differential systems of neutral type. Appl. Math. Comput. 162(2), 627–637 (2005)

    MathSciNet  MATH  Google Scholar 

  3. Ding, L.; He, Y.; Wu, M.; Ning, C.: Improved mixed-delay-dependent asymptotic stability criteria for neutral systems. IET Control Theory Appl. 9(14), 2180–2187 (2015)

    Article  MathSciNet  Google Scholar 

  4. Alaviani, S.S.: Delay-dependent exponential stability of linear time-varying neutral delay systems. IFAC-Papers OnLine 48(12), 177–179 (2015)

    Article  Google Scholar 

  5. Ren, Y.; Feng, Z.G.; Sun, G.H.: Improved stability conditions for uncertain neutral-type systems with time-varying delays. Int. J. Syst. Sci. 47(8), 1982–1993 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  6. Liu, L.P.: Improved results on delay-interval-dependent robust stability criteria for uncertain neutral-type systems with time-varying delays. ISA Trans. 60(3), 53–66 (2016)

    Article  Google Scholar 

  7. Qian, W.; Liu, J.; Sun, Y.X.; Fei, S.M.: A less conservative robust stability criteria for uncertain neutral systems with mixed delays. Math. Comput. Simul. 80(5), 1007–1017 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lu, R.Q.; Wu, H.Y.; Bai, J.J.: New delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. J. Frankl. Inst. 351(3), 1386–1399 (2014)

    Article  MathSciNet  Google Scholar 

  9. Chen, Y.G.; Qian, W.; Fei, S.M.: Improved robust stability conditions for uncertain neutral systems with discrete and distributed delays. J. Frankl. Inst. 352(7), 2634–2645 (2015)

    Article  MathSciNet  Google Scholar 

  10. Xiong, L.L.; Zhong, S.M.; Li, D.Y.: Novel delay-dependent asymptotical stability of neutral systems with nonlinear perturbations. J. Comput. Appl. Math. 232(2), 505–513 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu, Y.J.; Ma, W.B.; Mahmoud, M.S.; Lee, S.M.: Improved delay-dependent exponential stability criteria for neutral-delay systems with nonlinear uncertainties. Appl. Math. Model. 39(10–11), 3164–3174 (2015)

    Article  MathSciNet  Google Scholar 

  12. Gao, J.F.; Su, H.Y.; Ji, X.F.: Stability analysis for a class of neutral systems with mixed delays and sector-bounded nonlinearity. Nonlinear Anal.: Real World Appl. 9(5), 2350–2360 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Qiu, F.; Cao, J.D.; Hayat, T.: Delay-dependent stability of neutral system with mixed time-varying delays and nonlinear perturbations using delay-dividing approach. Cogn. Neurodyn. 9(1), 75–83 (2015)

    Article  Google Scholar 

  14. Cheng, J.; Zhu, H.; Zhong, S.M.; Li, G.H.: Novel delay-dependent robust stability criteria for neutral systems with mixed time-varying delays and nonlinear perturbations. Appl. Math. Comput. 219(14), 7741–7753 (2013)

    MathSciNet  MATH  Google Scholar 

  15. Qiu, F.; Cui, B.T.; Ji, Y.: Further results on robust stability of neutral system with mixed time-varying delays and nonlinear perturbations. Nonlinear Anal.: Real World Appl. 11(2), 895–906 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Lakshmanan, S.; Senthilkumar, T.; Balasubraman, M.: Improved results on robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations. Appl. Math. Model. 35(11), 5355–5368 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Balasubramaniam, P.; Lakshmanan, S.: Delay-interval-dependent robust-stability criteria for neutral stochastic neural networks with polytopic and linear fractional uncertainties. Int. J. Comput. Math. 88(10), 2001–2015 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang, X.J.; Cui, B.T.: A delay decomposition approach to robust absolute stability of neutral Lurie control system. Arab. J. Sci. Eng. 38(10), 2921–2928 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  19. Han, Q.L.: Improved stability criteria and controller design for linear neutral systems. Automatica 45(8), 1948–1952 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  20. Gu, B.; Sheng, V.S.; Tay, K.Y.; Romano, W.; Li, S.: Incremental support vector learning for ordinal regression. IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1403–1416 (2015)

    Article  MathSciNet  Google Scholar 

  21. Chen, H.B.; Wang, L.: New result on exponential stability for neutral stochastic linear system with time-varying delay. Appl. Math. Comput. 239(15), 320–325 (2015)

    MathSciNet  MATH  Google Scholar 

  22. Yu, Z.H.: The improved stability analysis of the backward Euler method for neutral stochastic delay differential equations. Int. J. Comput. Math. 90(7), 1489–1494 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  23. Xiong, L.L.; Zhang, H.Y.; Li, Y.K.: Improved stability and \(H\) infinity performance for neutral systems with uncertain Markovian jumpinging. Nonlinear Anal.: Hybrid Syst. 19, 13–25 (2016)

    MathSciNet  Google Scholar 

  24. Raja, R.; Zhu, Q.X.; Senthilraj, S.; Samidurai, R.: Improved stability analysis of uncertain neutral type neural networks with leakage delays and impulsive effects. Appl. Math. Comput. 266(1), 1050–1069 (2015)

    MathSciNet  Google Scholar 

  25. Zheng, C.D.; Wang, Y.; Wang, Z.S.: New stability results of neutral-type neural networks with continuously distributed delays and impulses. Int. J. Comput. Math. 91(9), 1880–1896 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  26. Sivasamy, R.; Rakkiyappan, R.: Improved stability criteria for neutral-type Lur’e systems with time-varying delays. Appl. Math. Lett. 38, 168–173 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  27. Liu, L.P.: Robust absolute stability criteria for uncertain Lur’e interval time-varying delay systems of neutral type. ISA Trans. 60, 2–11 (2016)

    Article  Google Scholar 

  28. Ma, T.H.; Zhou, J.J.; Tang, M.L.; Dhelaan, A.A.; et al.: Social network and tag sources based augmenting collaborative recommender system. IEICE Trans. Inf. Syst. E98–D(4), 902–910 (2015)

    Article  Google Scholar 

  29. Fang, M.; Park, J.H.: A multiple integral approach to stability of neutral time-delay systems. Appl. Math. Comput. 224, 714–718 (2013)

    MathSciNet  MATH  Google Scholar 

  30. Sun, J.; Liu, G.P.; Chen, J.; Rees, D.: Improved delay-range-dependent stability criteria for linear systems with time-varying delays. Automatica 46(2), 466–470 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  31. Kwon, O.M.; Lee, S.M.; Jark, J.H.: New approaches on stability criteria for neural networks with interval time-varying delays. Appl. Math. Comput. 218(19), 9953–9964 (2012)

    MathSciNet  MATH  Google Scholar 

  32. Zhang, B.Y.; Lam, J.; Xu, S.Y.: Relaxed results on reachable set estimation of time-delay systems with bounded peak inputs. Int. J. Robust Nonlinear Control 26, 1994–2007 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  33. Xia, Z.H.; Wang, X.H.; Sun, X.M.; Wang, Q.: A secure and dynamic multi-keyword ranked search scheme over encrypted cloud data. IEEE Trans. Parallel Distrib. Syst. 27(2), 340–352 (2015)

    Article  Google Scholar 

  34. Zeng, H.B.; He, Y.; Wu, M.; She, J.H.: New results on stability analysis for systems with discrete distributed delay. Automatica 60(3), 189–192 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  35. Park, J.H.; Kwon, O.; Park, J.H.; Lee, S.M.: Stability of time-delay systems via Wirtinger-based double integral inequality. Automatica 55(5), 204–208 (2015)

    Article  MathSciNet  Google Scholar 

  36. Li, T.; Wang, T.; Song, A.G.; Fei, S.M.: Delay-derivative-dependent stability for delayed neural networks with unbounded distributed delay. IEEE Trans. Neural Netw. 21(8), 1365–1371 (2010)

    Article  Google Scholar 

  37. Han, Q.L.; Yu, L.: Robust stability of linear neutral systems with nonlinear parameter perturbations. IEE Proc.-Control Theory Appl. 151(5), 539–546 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Science and Technology, Nanjing Forestry University, Nanjing, 210042, People’s Republic of China

    Ting Wang

  2. School of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, People’s Republic of China

    Tao Li

  3. School of Automation, Southeast University, Nanjing, 210096, People’s Republic of China

    Guobao Zhang & Shumin Fei

Authors
  1. Ting Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guobao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shumin Fei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ting Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, T., Li, T., Zhang, G. et al. Delay-Derivative-Dependent Stability for Neutral Systems with Time-Varying Delay and Nonlinearity. Arab J Sci Eng 42, 3033–3042 (2017). https://doi.org/10.1007/s13369-017-2462-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-017-2462-x

Keywords

Search

Navigation