[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Improved results on robust H ∞ control of uncertain discrete-time systems with time-varying delay

  • Published:
International Journal of Automation and Computing Aims and scope Submit manuscript

Abstract

In this paper, the robust H ∞ control problem for uncertain discrete-time systems with time-varying state delay is considered. Based on the Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the difference of the Lyapunov functional, a new less conservative sufficient condition for the existence of a robust H ∞ controller is obtained. Moreover, the cone complementary linearisation procedure is employed to solve the nonconvex feasibility problem. Finally, several numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. K. Gu, V. L. Kharitonov, J. Chen. Stability of Time-delay Systems, Birkhäuser, Boston, 2003.

    MATH  Google Scholar 

  2. L. Xie. Output Feedback H ∞ Control of Systems with Parameter Uncertainty. International Journal of Control, vol. 63, no. 4, pp. 741–750, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  3. L. Yu, Q. L. Han, S. Yu, J. Gao. Delay Dependent Conditions for Robust Absolute Stability of Uncertain Time-delay Systems. In Proceedings of the 42nd IEEE Conference on Decision and Control, IEEE Press, vol. 6, pp. 6033–6037, 2003.

    Google Scholar 

  4. E. Fridman, U. Shaked. Delay-dependent Stability and H ∞ Control: Constant and Time-varying Delays. International Journal of Control, vol. 76, no. 1, pp. 48–60, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  5. Y. S. Lee, Y. S. Moon, W. H. Moon, P. G. Park. Delaydependent Robust H ∞ Control for Uncertain Systems with a State-delay. Automatica, vol. 40, no. 1, pp. 65–72, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  6. Y. He, M. Wu, J. H. She, G. P. Liu. Delay-dependent Robust Stability Criteria for Uncertain Neutral Systems with Mixed Delays. Systems & Control Letters, vol. 51, no. 1, pp. 57–65, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  7. Y. He, M. Wu, J. H. She, G. P. Liu. Parameter-dependent Lyapunov Functional for Stability of Time-delay Systems with Polytopic-type Uncertainties. IEEE Transactions on Automatic Control, vol. 49, no. 5, pp. 828–832, 2004.

    Article  MathSciNet  Google Scholar 

  8. S. Xu, J. Lam, Y. Zou. New Results on Delay-dependent Robust H ∞ Control for Systems with Time-varying Delays. Automatica, vol. 42, no. 2, pp. 343–348, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  9. Q. L. Han, D. Yue. Absolute Stability of Luré Systems with Time-varying Delay. IET Control Theory & Applications, vol. 1, no. 3, pp. 854–859, 2007.

    Article  MathSciNet  Google Scholar 

  10. S. H. Song, J. K. Kim, C. H. Yim, H. C. Kim. H t8 Control of Discrete-time Linear Systems with Time-varying Delays in State. Automatica, vol. 35, no. 9, pp. 1587–1591, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  11. H. Gao, J. Lam, C. Wang, Y. Wang. Delay-dependent Output-feedback Stabilisation of Discrete-time Systems with Time-varying State Delay. IEE Proceedings: Control Theory and Applications, vol. 151, no. 6, pp. 691–698, 2004.

    Article  MathSciNet  Google Scholar 

  12. E. Fridman, U. Shaked, D. Popescu, V. Rasvan. Delaydependent H ∞ Control of Uncertain Discrete Delay Systems. European Journal of Control, vol. 11, no. 1, pp. 29–39, 2005.

    Article  MathSciNet  Google Scholar 

  13. X. G. Liu, R. R. Marin, M. Wu, M. L. Tang. Delaydependent Robust Stabilisation of Discrete-time Systems with Time-varying Delay. IEE Proceedings: Control Theory and Applications, vol. 153, no. 6, pp. 689–702, 2006.

    Article  MathSciNet  Google Scholar 

  14. X.M. Zhang, M. Wu, J. H. She, D. S. Han. Delay-dependent Robust H-infinity Control for Discrete-time Uncertain Systems with Time-varying State Delays. Journal of Theory and Applications, vol. 4, no. 4, pp. 355–360, 2006.

    Article  MATH  Google Scholar 

  15. H. Gao, T. Chen. New Results on Stability of Discrete-time Systems with Time-varying State Delay. IEEE Transactions on Automatic Control, vol. 52, no. 2, pp. 328–334, 2007.

    Article  MathSciNet  Google Scholar 

  16. E. K. Boukas. State Feedback Stabilization of Nonlinear Discrete-time Systems with Time-varying Time Delay. Nonlinear Analysis, vol. 66, no. 6, pp. 1341–1350, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  17. Y. He, M. Wu, Q. L. Han, J. H. She. Delay-dependent H ∞ Control of Linear Discrete-time Systems with an Intervallike Time-varying Delay. International Journal of Systems Science, vol. 39, no. 4, pp. 427–436, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  18. M. S. Mahmoud. Resilient Control of Uncertain Dynamical Systems, Springer-Verlag, Berlin, 2004.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Henan Institute of Science and Technology, Xinxiang, 453003, PRC

    Yong-Gang Chen

  2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, PRC

    Wen-Lin Li

Authors
  1. Yong-Gang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wen-Lin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong-Gang Chen.

Additional information

This work was supported by National Natural Science Foundation of China (No. 60850004).

Yong-Gang Chen received his B. Sc. and M. Sc. degrees from the College of Mathematics and Information at Henan Normal University, Xinxiang, PRC, in 2003 and 2006, respectively. He is currently a faculty member of Henan Institute of Science and Technology, PRC.

His research interests include time-delay systems, neural networks, and robust control.

Wen-Lin Li received his M. Sc. degree from the Department of Mathematics at Shandong Normal University, Jinan, PRC, in 1982, and Ph.D. degree in automatic control engineering at Beihang University, Beijing, PRC, in 1993. He is currently a professor with the College of Mathematics and Information Science at Henan Normal University, PRC.

His research interests include variable structure control, fuzzy control, time-delay systems, and chaos synchronization control.

About this article

Cite this article

Chen, YG., Li, WL. Improved results on robust H ∞ control of uncertain discrete-time systems with time-varying delay. Int. J. Autom. Comput. 6, 103–108 (2009). https://doi.org/10.1007/s11633-009-0103-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11633-009-0103-x

Keywords

Search

Navigation