Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

Exponential H ∞ control for singular systems with time-varying delay

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper studies the exponential admissibility and H ∞ control problems for a class of singular systems with time-varying delay in state. Firstly, an exponential admissibility criterion is obtained based on linear matrix inequalities (LMIs). It is worth mentioning that the derivative of the time-varying delay does not need to be smaller than one. Based on the proposed condition, a new delay-dependent H ∞ controller is also given, which guarantees the admissibility and the H ∞ performance γ. Numerical examples are given to illustrate the effectiveness 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
EUR 32.99 /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 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. W. Yu, S. Liu, and F. Zhang, “Global output feedback regulation of uncertain nonlinear systems with unknown time delay,” International Journal of Control, Automation and Systems, vol. 13, no. 2, pp. 327–335, 2015. [click]

    Article  Google Scholar 

  2. M. Kazerooni, A. Khayatian, and A. A. Safavi, “Robust delay dependent fault estimation for a class of interconnected nonlinear time delay systems,” International Journal of Control, Automation and Systems, vol. 14, no. 2, pp. 569–578, 2016. [click]

    Article  Google Scholar 

  3. Y. Sheng, Y. Shen, and M. Zhu, “Delay-dependent global exponential stability for delayed recurrent neural networks,” IEEE Transactions on Neural Networks and Learning Systems, 2016.

    Google Scholar 

  4. X. Zhang, Y. Han, L. Wu, and J. Zou, “M-matrix-based globally asymptotic stability criteria for genetic regulatory networks with time-varying discrete and unbounded distributed delays,” Neurocomputing, vol. 174, pp. 1060–1069, 2016. [click]

    Article  Google Scholar 

  5. S. Xu and J. Lam, Robust Control and Filtering of Singular Systems, Springer, Berlin, 2006.

    MATH  Google Scholar 

  6. J. Cheng, H. Wang, S. Chen, and J. Yang, “Robust delayderivative-dependent state-feedback control for a class of continuous-time system with time-varying delays,” Neurocomputing, vol. 173, pp. 827–834, 2016. [click]

    Article  Google Scholar 

  7. J. Cheng, H. Zhu, S. Zhong, Y. Zeng, and X. Dong, “Finitetime H ∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals,” ISA transactions, vol. 52, no. 6, pp. 768–774, 2013.

    Article  Google Scholar 

  8. X. Gao, L. Lian, and W. Qi, “H ∞ control for sochastic timedelayed Markovian switching systems with partly known transition rates and input saturation,” International Journal of Control, Automation and Systems, vol. 14, no. 3, pp. 637–646, 2016. [click]

    Article  Google Scholar 

  9. L. Dai, Singular Control Systems, Springer-Verlag, Berlin, Germany, 1989.

    Book  MATH  Google Scholar 

  10. F. Lewis, “A survey of linear singular systems,” Circuits Syst. Signal Process, vol. 5, no. 1, pp. 3–36, 1986. [click]

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Haidar and E. K. Boukas, “Exponential stability of singular systems with multiple time-varying delays,” Automatica, vol. 45, no. 2, pp. 539–545, 2009. [click]

    Article  MathSciNet  MATH  Google Scholar 

  12. X. Ding, Xiu Liu, and S. Zhong, “Delay-independent criteria for exponential admissibility of switched descriptor delayed systems,” Applied Mathematics and Computation, vol. 228, pp. 432–445, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Zhao, Z. Hu, and L. Zhang, “Stability and stabilization for discrete-time singular systems with infinite distributed delays and actuator failures,” International Journal of Control, Automation and Systems, vol. 10, no. 4, pp. 721–726, 2012. [click]

    Article  Google Scholar 

  14. J. Zhao, L. Zhang, and X. Qi, “A necessary and sufficient condition for stabilization of switched descriptor time-delay systems under arbitrary switching,” Asian Journal of Control, vol. 18, no. 1, pp. 266–272, 2016. [click]

    Article  MathSciNet  MATH  Google Scholar 

  15. J. X. Lin, X. L. Zhao, and S. M. Fei, “New delay-rangedependent exponential estimates for singular systems with time-varying delay,” International Journal of Control, Automation, and Systems, vol. 9, no. 2, 218–227, 2011. [click]

    Article  Google Scholar 

  16. M. Kchaou, F. Tadeo, M. Chaabane, and A. Toumi, “Delaydependent robust observer-based control for discrete-time uncertain singular systems with interval time-varying state delay,” International Journal of Control, Automation and Systems, vol. 12, no. 1, pp. 12–22, 2014. [click]

    Article  Google Scholar 

  17. Y. Ding, H. Zhu, and S. Zhong, “Exponential stabilization using sliding mode control for singular systems with timevarying delays and nonlinear perturbations”, Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 10, pp. 4099–4107, 2011. [click]

    Article  MathSciNet  MATH  Google Scholar 

  18. Y. Cui, J. Lam, Z. Feng, and J. Shen, “Robust admissibility and admissibilisation of uncertain discrete singular timedelay systems,” International Journal of Systems Science, vol. 47, no. 15, 1-10, 2015.

    Google Scholar 

  19. Z. Hu, H. Zhu, and J. Zhao, “Further results on H ∞ filtering for a class of discrete-time singular systems with interval time-varying delay,” Circuits, Systems, and Signal Processing, vol. 32, no. 3, pp. 1081–1095, 2013.

    Article  MathSciNet  Google Scholar 

  20. Z. G. Wu, H. Y. Su, and J. Chu, “H ∞ filtering for singular systems with time-varying delay,” International Journal of Robust and Nonlinear Control, vol. 20, no. 11, pp. 1269–1284, 2010. [click]

    Article  MathSciNet  MATH  Google Scholar 

  21. X. Zhu, Y. Wang, and Y. Gan, “H ∞ filtering for continuoustime singular systems with time-varying delay,” International Journal of Adaptive Control and Signal Processing, vol. 25, no. 2, pp. 137–154, 2011. [click]

    Article  MathSciNet  Google Scholar 

  22. L. G. Wu and W. X. Zheng, “Passivity-based sliding mode control of uncertain singular time-delay systems,” Automatica, vol. 45, no. 9, pp. 2120–2127, 2009. [click]

    Article  MathSciNet  MATH  Google Scholar 

  23. Z. G. Wu, J. H. Park, H. Y. Su, and J. Chu, “Delaydependent passivity for singular Markov jump systems with time-delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 3, pp. 669–681, 2013. [click]

    Article  MathSciNet  MATH  Google Scholar 

  24. Z. G. Wu, J. H. Parka, H. Y. Su, and J. Chu, “Reliable passive control for singular systems with time-varying delays,” Journal of Process Control, vol. 23, no. 8, pp. 1217–1228, 2013. [click]

    Article  Google Scholar 

  25. X. Dong and M. Xiao, “H ∞ control of singular systems via delta operator method,” International Journal of Control, Automation and Systems, vol. 13, no. 3, pp. 643–651, 2015. [click]

    Article  Google Scholar 

  26. M. Chadli and M. Darouach, “Novel bounded real lemma for discrete-time descriptor systems: application to H ∞ control design,” Automatica, vol. 48, no. 2, pp. 449–453, 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  27. Y. Zhang, P. Shi, S. K. Nguang, and Y. Song, “Robust finite-time H ∞ control for uncertain discrete-time singular systems with Markovian jumps,” IET Control Theory & Applications, vol. 8, no. 12, pp. 1105–1111, 2014. [click]

    Article  MathSciNet  Google Scholar 

  28. L. H. Xie and C. E. de Souza, “Robust H ∞ control for linear systems with norm-bounded time-varying uncertainty,” IEEE Trans. Autom. Control, vol. 37, no. 8, pp. 1188–1191, 1992. [click]

    Article  MathSciNet  MATH  Google Scholar 

  29. S. Kririm, A. Hmamed, and F. Tadeo, “Analysis and design of H ∞ controllers for 2D singular systems with delays,” Circuits, Systems, and Signal Processing, vol. 35, no. 5, pp. 1579–1592, 2016.

    Article  MATH  Google Scholar 

  30. H. Chen and P. Hu, “New result on exponential stability for singular systems with two interval time-varying delays,” IET Control Theory & Applications, vol. 7, no. 15, pp. 1941–1949, 2013.

    Article  MathSciNet  Google Scholar 

  31. L. V. Hien, L. H. Vu, and V. N. Phat, “Improved delaydependent exponential stability of singular systems with mixed interval time-varying delays,” IET Control Theory & Applications, vol. 9, no. 9, pp. 1364–1372, 2015. [click]

    Article  MathSciNet  Google Scholar 

  32. Z. G. Wu, H. Y. Su, J. H. Park, and J. Chu, “Dissipativity analysis for singular systems with time-varying delays,” Applied Mathematics and Computation, vol. 218, pp. 4605–4613, 2011. [click]

    Article  MathSciNet  MATH  Google Scholar 

  33. E. K. Boukas, Control of Singular Systems with Random Abrupt Changes, Springer, New York, 2008.

    MATH  Google Scholar 

  34. H. Li, Y. Gao, P. Shi, and X. Zhao, “Output-feedback control for T-S fuzzy delta operator systems with time-varying delays via an input-output approach,” IEEE Transactions on Fuzzy Systems, vol. 23, no. 4, pp. 1100–1112, 2015. [click]

    Article  Google Scholar 

  35. H. Li, Y. Gao, L. Wu, and H. K. Lam, “Fault detection for T-S fuzzy time-delay systems: delta operator and inputoutput methods,” IEEE transactions on cybernetics, vol. 45, no. 2, pp. 229–241, 2015.

    Article  Google Scholar 

  36. X. Su, P. Shi, L. Wu, and Y. Song, “A novel control design on discrete-time Takagi-Sugeno fuzzy systems with timevarying delays,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 4, pp. 655–671, 2013.

    Article  Google Scholar 

  37. M. Chadli, H. R. Karimi, and P. Shi, “On stability and stabilization of singular uncertain Takagi-Sugeno fuzzy systems,” Journal of the Franklin Institute, vol. 351, no. 3, pp. 1453–1463, 2014. [click]

    Article  MathSciNet  Google Scholar 

  38. Y. Liu, Y. Kao, S. Gu, and H. R. Karimi, “Soft variable structure controller design for singular systems,” Journal of the Franklin Institute, vol. 352, no. 4, pp. 1613–1626, 2015. [click]

    Article  MathSciNet  Google Scholar 

  39. Y. Liu, Y. Kao, H. R. Karimi, and Z. Gao, “Input-to-state stability for discrete-time nonlinear switched singular systems,” Information Sciences, vol. 358, pp. 18–28, 2016. [click]

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan, 430023, China

    Jiemei Zhao

  2. 709th Research Institute of China Shipbuilding Industry Corporation, Wuhan, 430074, China

    Zhonghui Hu

Authors
  1. Jiemei Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhonghui Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiemei Zhao.

Additional information

Recommended by Associate Editor Sing Kiong Nguang under the direction of Editor Myo Taeg Lim. This work was supported by the Natural Science Foundation of Hubei Province of China(2016CFB273), the Research and Innovation Initiatives of WHPU (2015d9).

Jiemei Zhao received her M.S. degree in Applied Mathematics and the Ph.D. degree in Systems Engineering from the Harbin Engineering University, Harbin, China, in 2008 and 2013, respectively. Since 2013, she is a lecturer with the School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan, China. Her research interests include nonlinear control systems, singular systems, neural networks and memristors.

Zhonghui Hu received his Ph.D. degree in Systems Engineering from the Harbin Engineering University, Harbin, China, in 2013. Since 2013, he works at the 709th Research Institute of China Shipbuilding Industry Corporation, China. His research interests include nonlinear control systems.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, J., Hu, Z. Exponential H ∞ control for singular systems with time-varying delay. Int. J. Control Autom. Syst. 15, 1592–1599 (2017). https://doi.org/10.1007/s12555-016-0297-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-016-0297-y

Keywords

Search

Navigation