Skip to main content
SpringerLink
Log in

Robust Exponential Stabilization Results for Impulsive Neutral Time-Delay Systems with Sector-Bounded Nonlinearity

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, the problem of robust exponential stabilization analysis for nonlinear neutral systems with time-varying delays under impulsive control is addressed. Sufficient delay-dependent exponential stabilization results are derived in terms of linear matrix inequalities by constructing suitable Lyapunov–Krasovskii functional. The control gain matrices are designed using impulsive state-feedback control approach. Also, the nonlinear function is assumed to satisfy the sector-bounded condition which includes Lipschitz condition as a special case. Further numerical examples are provided to show the effectiveness 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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. A. Bellen, N. Guglielmi, A.E. Ruehli, Methods for linear systems of circuit delay differential equations of neutral type. IEEE Trans. Circuits Syst. 46(1), 212–216 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  2. E.K. Boukas, Z.K. Liu, P. Shi, Delay-dependent stability and output feedback stabilization of Markov jump system with time-delay. IEE Proc. Control Theory Appl. 149(5), 379–386 (2002)

    Article  Google Scholar 

  3. W.H. Chen, F. Chen, X. Lu, Exponential stability of a class of singularly perturbed stochastic time-delay systems with impulse effect. Nonlinear Anal. Real World Appl. 11(5), 3463–3478 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  4. W.H. Chen, W.X. Zheng, Exponential stability of nonlinear time-delay systems with delayed impulse effects. Automatica 47(5), 1075–1083 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  5. Y. Chen, H. Xu, Exponential stability analysis and impulsive tracking control of uncertain time-delayed systems. J. Glob. Optim. 52(2), 323–334 (2012)

    Article  MATH  Google Scholar 

  6. P. Cheng, F. Deng, Y. Peng, Robust exponential stability and delayed-state-feedback stabilization of uncertain impulsive stochastic systems with time-varying delay. Commun. Nonlinear Sci. Numer. Simul. 17(12), 4740–4752 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  7. Y. Dong, J. Liu, Exponential stabilization of uncertain nonlinear time-delay systems. Adv. Differ. Equ. 180, 1–15 (2012)

    Google Scholar 

  8. J. Gao, H. Su, X. Ji, J. Chu, 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  MATH  MathSciNet  Google Scholar 

  9. K. Gu, L. Kharitonov, J. Chen, Stability of Time Delay Systems (Birkhauser, Boston, 2003)

    Book  MATH  Google Scholar 

  10. J.K. Hale, S.M. Verduyn Lunel, Introduction to Functional Differential Equations (Springer, New York, 1993)

    Book  MATH  Google Scholar 

  11. Q.L. Han, Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica 41(12), 2171–2176 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  12. H.K. Khalil, Nonlinear Systems (Prentice Hall, New Jersey, 1996)

    Google Scholar 

  13. O.M. Kwon, M.J. Park, J.H. Park, S.M. Lee, E.J. Cha, New delay-partitioning approaches to stability criteria for uncertain neutral systems with time-varying delays. J. Frankl. Inst. 349(9), 2799–2823 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  14. V. Lakshmikanthan, D.D. Bainov, P.S. Simeonov, Theory of Impulsive Differential Equations (World Scientific, Singapore, 1989)

    Book  Google Scholar 

  15. C. Li, L. Chen, K. Aihara, Impulsive control of stochastic systems with applications in chaos control, chaos synchronization, and neural networks. Chaos 18(2), 023132 (2008)

    Article  MathSciNet  Google Scholar 

  16. B. Li, D. Li, D. Xu, Stability analysis for impulsive stochastic delay differential equations with Markovian switching. J. Frankl. Inst. 350(7), 1848–1864 (2013)

    Article  Google Scholar 

  17. X. Li, R. Rakkiyappan, Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays. Commun. Nonlinear Sci. Numer. Simul. 18(16), 1515–1523 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  18. B. Liu, K.L. Teo, X. Liu, Robust exponential stabilization for large-scale uncertain impulsive systems with coupling time-delays. Nonlinear Anal. 68(5), 1169–1183 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  19. Y. Liu, S. Zhao, J. Lu, A new fuzzy impulsive control of chaotic systems based on T–S fuzzy model. IEEE Trans. Fuzzy Syst. 19(2), 393–398 (2011)

    Article  MathSciNet  Google Scholar 

  20. P.L. Liu, A delay decomposition approach to stability analysis of neutral systems with time-varying delay. Appl. Math. Model. 37(7), 5013–5026 (2013)

    Article  MathSciNet  Google Scholar 

  21. S. Liu, Z. Xiang, Exponential \(H_{\infty }\) output tracking control for switched neutral system with time-varying delay and nonlinear perturbations. Circuits Syst. Signal Process. 32(1), 103–121 (2013)

    Article  MathSciNet  Google Scholar 

  22. X. Liu, P. Stechlinski, Hybrid control of impulsive systems with distributed delays. Nonlinear Anal. Hybrid Syst. 11, 57–70 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  23. X. Lou, Q. Ye, B. Cui, Impulsive stabilization of fuzzy neural networks with time-varying delays. Arab. J. Math. 2(1), 65–79 (2013)

    Article  MathSciNet  Google Scholar 

  24. J. Lu, D.W.C. Ho, J. Cao, J. Kurths, Single impulsive controller for globally exponential synchronization of dynamical networks. Nonlinear Anal. Real World Appl. 14(1), 581–593 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  25. P.T. Nam, V.N. Phat, An improved stability criterion for a class of neutral differential equations. Appl. Math. Lett. 22(1), 31–35 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  26. S. Peng, Y. Zhang, S. Yu, Global mean-square exponential stabilization of stochastic system with time delay via impulsive control. Asian J. Control. 14(1), 288–299 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  27. R. Rakkiyappan, P. Balasubramaniam, J. Cao, Global exponential stability results for neutral-type impulsive neural networks. Nonlinear Anal. Real World Appl. 11(1), 122–130 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  28. L. Wu, D.W.C. Ho, C.W. Li, Sliding mode control of switched hybrid systems with stochastic perturbation. Syst. Control Lett. 60(8), 531–539 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  29. T. Yang, L.O. Chua, Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. IEEE Trans. Circuits Syst. 44(10), 976–988 (1997)

    Article  MathSciNet  Google Scholar 

  30. J. Yang, S. Zhong, W. Luo, Mean square stability analysis of impulsive stochastic differential equations with delays. J. Comput. Appl. Math. 216(2), 474–483 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  31. J. Yao, Y. Su, Y. Guo, J. Zhang, Exponential synchronisation of hybrid impulsive and switching dynamical networks with time delays. IET Control Theory Appl. 7(4), 508–514 (2013)

    Article  MathSciNet  Google Scholar 

  32. J. Yu, C. Hu, H. Jiang, Z. Teng, Stabilization of nonlinear systems with time-varying delays via impulsive control. Neurocomputing 12511, 68–71 (2014)

    Article  Google Scholar 

  33. X.M. Zhang, Q.L. Han, A new stability criterion for a partial element equivalent circuit model of neutral type. IEEE Trans. Circuits Syst. 56(10), 798–802 (2009)

    Article  Google Scholar 

  34. H. Zhang, M. Dong, Y. Wang, N. Sun, Stochastic stability analysis of neutral-type impulsive neural networks with mixed time-varying delays and Markovian jumping. Neurocomputing 73(13), 2689–2695 (2010)

    Article  Google Scholar 

  35. Z. Zhang, X. Liu, Stability analysis and synthesis of discrete impulsive switched systems with time-varying delays and parameter uncertainty. Circuits Syst. Signal Process. 32(1), 61–81 (2013)

    Article  Google Scholar 

  36. Q. Zhu, J. Cao, Stability of Markovian jump neural networks with impulse control and time varying delays. Nonlinear Anal. Real World Appl. 13(5), 2259–2270 (2012)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work is supported by the University Grants Commission—Special Assistance Program (Departmental Research Support II), Government of India, New Delhi under the Grant No. F.510/2/DRS/2009(SAP-I). The authors are very much thankful to the Editor-in-chief, Associate editor and anonymous reviewers for their careful reading, constructive comments, and fruitful suggestions to improve the quality of this manuscript.

Author information

Authors and Affiliations

  1. Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram , 624 302, Tamil Nadu, India

    P. Balasubramaniam & R. Krishnasamy

Authors
  1. P. Balasubramaniam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Krishnasamy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Balasubramaniam.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Balasubramaniam, P., Krishnasamy, R. Robust Exponential Stabilization Results for Impulsive Neutral Time-Delay Systems with Sector-Bounded Nonlinearity. Circuits Syst Signal Process 33, 2741–2759 (2014). https://doi.org/10.1007/s00034-014-9771-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-014-9771-z

Keywords

Search

Navigation