Skip to main content
SpringerLink
Log in

Stability of Neutral Systems

  • Chapter
Stability Analysis and Robust Control of Time-Delay Systems

  • 2544 Accesses

Abstract

A neutral system is a system with a delay in both the state and the derivative of the state, with the one in the derivative being called a neutral delay. That makes it more complicated than a system with a delay in only the state. Neutral delays occur not only in physical systems, but also in control systems, where they are sometimes artificially added to boost the performance. For example, repetitive control systems constitute an important class of neutral systems [1]. Stability criteria for neutral systems can be classified into two types: delay-independent [2–4] and delay-dependent [5–24]. Since the delayindependent type does not take the length of a delay into consideration, it is generally conservative. The basic methods for studying delay-dependent criteria for neutral systems are similar to those used to study linear systems, with the main ones being fixed model transformations. As mentioned in Chapter 1, the four types of fixed model transformations impose limitations on possible solutions to delay-dependent stability problems.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Hara, Y. Yamamoto, T. Omata, and M. Nakano. Repetitive control system: a new type servo system for periodic exogenous signals. IEEE Transactions on Automatic Control, 33(7): 659–668, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  2. G. D. Hu and G. D. Hu. Some simple stability criteria of neutral delaydifferential systems. Applied Mathematics and Computation, 80(2–3): 257–271, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  3. G. D. Hui and G. D. Hu. Simple criteria for stability of neutral systems with multiple delays. International Journal of Systems Science, 28(12): 1325–1328, 1997.

    Article  MATH  Google Scholar 

  4. M. S. Mahmoud. Robust H ∞ control of linear neutral systems. Automatica, 36(5): 757–764, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  5. W. H. Chen and W. X. Zheng. Delay-dependent robust stabilization for uncertain neutral systems with distributed delays. Automatica, 43(1): 95–104, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  6. C. H. Lien. New stability criterion for a class of uncertain nonlinear neutral time-delay systems. International Journal of Systems Science, 32(2): 215–219, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  7. C. H. Lien, K. W. Yu, and J. G. Hsieh. Stability conditions for a class of neutral systems with multiple delays. Journal of Mathematical Analysis and Applications, 245(1): 20–27, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  8. J. D. Chen, C. H. Lien, K. K. Fan, and J. H. Chou. Criteria for asymptotic stability of a class of neutral systems via an LMI approach. IEE Proceedings-Control Theory and Application, 148(6): 442–447, 2001.

    Article  Google Scholar 

  9. J. H. Park. A new delay-dependent criterion for neutral systems with multiple delays. Journal of Computational and Applied Mathematics, 136(1–2): 177–184, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  10. S. I. Niculescu. On delay-dependent stability under model transformations of some neutral linear systems. International Journal of Control, 74(6): 608–617, 2001.

    Article  MathSciNet  Google Scholar 

  11. S. I. Niculescu. Optimizing model transformations in delay-dependent analysis of neutral systems: A control-based approach. Nonlinear Analysis, 47(8): 5378–5390, 2001.

    Article  MathSciNet  Google Scholar 

  12. E. Fridman. New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems. Systems & Control Letters, 43(4): 309–319, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  13. Q. L. Han. On delay-dependent stability for neutral delay-differential systems. International Journal of Applied Mathematics and Computer Science, 11(4): 965–976, 2001.

    MATH  MathSciNet  Google Scholar 

  14. Q. L. Han. Robust stability of uncertain delay-differential systems of neutral type. Automatica, 38(4): 718–723, 2002.

    Article  Google Scholar 

  15. J. H. Park. Stability criterion for neutral differential systems with mixed multiple time-varying delay arguments. Mathematics and Computers in Simulation, 59(5): 401–412, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  16. Q. L. Han. Stability criteria for a class of linear neutral systems with timevarying discrete and distributed delays. IMA Journal of Mathematical Control and Information, 20(4): 371–386, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  17. D. Ivânescu, S. I. Niculescu, L. Dugard, J. M. Dionc, and E. I. Verriestd. On delay-dependent stability for linear neutral systems. Automatica, 39(2): 255–261, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  18. E. Fridman and U. Shaked. A descriptor system approach to H ∞ control of linear time-delay systems. IEEE Transactions on Automatic Control, 47(2): 253–270, 2002.

    Article  MathSciNet  Google Scholar 

  19. E. Fridman and U. Shaked. Delay-dependent stability and H ∞ control: constant and time-varying delays. International Journal of Control, 76(1): 48–60, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  20. Q. L. Han. Robust stability for a class of linear systems with time-varying delay and nonlinear perturbations. Computers & Mathematics with Applications, 47(8–9): 1201–1209, 2004.

    Article  MATH  Google Scholar 

  21. Q. L. Han and L. Yu. Robust stability of linear neutral systems with nonlinear parameter perturbations. IEE Proceedings-Control Theory & Applications, 151(5): 539–546, 2004.

    Article  Google Scholar 

  22. Q. L. Han. A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays. Automatica, 40(10): 1791–1796, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  23. Y. He, M. Wu, J. H. She, and G. P. Liu. Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Systems & Control Letters, 51(1): 57–65, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  24. Y. He, M. Wu, and J. H. She. Delay-dependent robust stability and stabilization of uncertain neutral systems. Asian Journal of Control, 10(3): 376–383, 2008.

    Article  MathSciNet  Google Scholar 

  25. Y. He and M. Wu. Delay-dependent robust stability for neutral systems with mixed discrete-and neutral-delays. Journal of Control Theory and Applications, 2(4): 386–392, 2004.

    Article  MathSciNet  Google Scholar 

  26. M. Wu, Y. He, and J. H. She. New delay-dependent stability criteria and stabilizing method for neutral systems. IEEE Transactions on Automatic Control, 49(12): 2266–2271, 2004.

    Article  MathSciNet  Google Scholar 

  27. Y. He, Q. G. Wang, C. Lin, and M. Wu. Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems. International Journal of Robust and Nonlinear Control, 15(18): 923–933, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  28. J. K. Hale and S. M. Verduyn Lunel. Introduction to Functional Differential Equations. New York: Springer-Verlag, 1993.

    MATH  Google Scholar 

  29. Y. He, Q. G. Wang, L. Xie, and C. Lin. Further improvement of free-weighting matrices technique for systems with time-varying delay. IEEE Transactions on Automatic Control, 52(2): 293–299, 2007.

    Article  MathSciNet  Google Scholar 

  30. Y. He, G. P. Liu, and D. Rees. Augmented Lyapunov functional for the calculation of stability interval for time-varying delay. IET Proceedings: Control Theory & Applications, 1(1): 381–386, 2007.

    Article  MathSciNet  Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Science Press Beijing and Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2010). Stability of Neutral Systems. In: Stability Analysis and Robust Control of Time-Delay Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03037-6_5

Download citation

Publish with us

Policies and ethics

Search

Navigation