http://iet.metastore.ingenta.com
1887

Control scheme for LTI systems with Lipschitz non-linearity and unknown time-varying input delay

Control scheme for LTI systems with Lipschitz non-linearity and unknown time-varying input delay

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

In this study, the authors propose a control structure for a class of linear time-invariant (LTI) systems with Lipschitz non-linearity and unknown time-varying input delay. This scheme considers the worst-case scenario in control design with truncated prediction feedback approach, and takes into account the information of the lower bound of delay in the stability analysis. A finite-dimensional controller is constructed, requiring neither the non-linear function nor the exact delay function. The truncated prediction deviation is minimised by employing the delay range, and then bounded by integral construction and related techniques. Within the framework of Lyapunov–Krasovskii functionals, sufficient delay–range-dependent conditions are derived for the closed-loop system to guarantee the global stability. Two numerical examples are given to validate the proposed control design.

References

    1. 1)
      • 1. Gu, K., Chen, J., Kharitonov, V.L.: ‘Stability of time-delay systems’ (Springer Science & Business Media, London, 2003).
    2. 2)
      • 2. Richard, J.: ‘Time-delay systems: an overview of some recent advances and open problems’, Automatica, 2003, 39, pp. 16671694.
    3. 3)
      • 3. Fridman, E., Shaked, U.: ‘An improved stabilization method for linear time-delay systems’, IEEE Trans. Autom. Control, 2002, 47, pp. 19311937.
    4. 4)
      • 4. Fridman, E., Shaked, U.: ‘Delay-dependent stability and H control: constant and time-varying delays’, Int. J. Control, 2003, 76, pp. 4860.
    5. 5)
      • 5. Xia, Y., Jia, Y.: ‘Robust sliding-mode control for uncertain time-delay systems: an LMI approach’, IEEE Trans. Autom. Control, 2003, 48, pp. 10861091.
    6. 6)
      • 6. Yue, D., Han, Q.L.: ‘Delayed feedback control of uncertain systems with time-varying input delay’, Automatica, 2005, 41, pp. 233240.
    7. 7)
      • 7. Gao, H., Chen, T., Lam, J.: ‘A new delay system approach to network-based control’, Automatica, 2008, 44, pp. 3952.
    8. 8)
      • 8. Liang, J., Liu, X.: ‘Robust stabilisation for a class of stochastic two-dimensional non-linear systems with time-varying delays’, IET Control Theory Appl., 2013, 7, pp. 16991710.
    9. 9)
      • 9. Li, T., Qian, W., Wang, T., , et al: ‘Further results on delay-dependent absolute and robust stability for time-delay Lur'e system’, Int. J. Robust Nonlinear Control, 2014, 24, pp. 33033316.
    10. 10)
      • 10. Wang, L., Wang, Z., Huang, T., , et al: ‘An event-triggered approach to state estimation for a class of complex networks with mixed time delays and nonlinearities’, IEEE Trans. Cybern., 2016, 46, pp. 24972508.
    11. 11)
      • 11. Manitius, A., Olbrot, A.: ‘Finite spectrum assignment problem for systems with delays’, IEEE Trans. Autom. Control, 1979, 24, pp. 541552.
    12. 12)
      • 12. Artstein, Z.: ‘Linear systems with delayed controls: a reduction’, IEEE Trans. Autom. Control, 1982, 27, pp. 869879.
    13. 13)
      • 13. Krstic, M.: ‘Lyapunov stability of linear predictor feedback for time-varying input delay’, IEEE Trans. Autom. Control, 2010, 55, pp. 554559.
    14. 14)
      • 14. Mazenc, F., Niculescu, S.I., Krstic, M.: ‘Lyapunov–Krasovskii functionals and applications to input delay compensation for linear-time-invariant systems’, Automatica, 2012, 48, pp. 13171323.
    15. 15)
      • 15. Léchappé, V., Moulay, E., Plestan, F., , et al: ‘New predictive scheme for the control of LTI systems with input delay and unknown disturbances’, Automatica, 2015, 52, pp. 179184.
    16. 16)
      • 16. Bekiaris-Liberis, N., Krstic, M.: ‘Compensation of time-varying input and state delays for nonlinear systems’, J. Dyn. Syst. Meas. Control, 2012, 134, p. 011009.
    17. 17)
      • 17. Besançon, G., Georges, D., Benayache, Z.: ‘Asymptotic state prediction for continuous-time systems with delayed input and application to control’. Proc. 2007 European Control Conf. (ECC), 2007, pp. 17861791.
    18. 18)
      • 18. Léchappé, V., Moulay, E., Plestan, F.: ‘Dynamic observation-prediction for LTI systems with a time-varying delay in the input’. Proc. 55th IEEE Conf. Decision Control, CDC, Las Vegas, NV, 2016, pp. 23022307.
    19. 19)
      • 19. Lin, Z., Fang, H.: ‘On asymptotic stability of linear systems with delayed input’, IEEE Trans. Autom. Control, 2007, 52, pp. 9981013.
    20. 20)
      • 20. Zhou, B., Lin, Z., Duan, G.: ‘Stabilization of linear systems with input delay and saturation - -a parametric Lyapunov equation approach’, Int. J. Robust Nonlinear Control, 2010, 20, pp. 15021519.
    21. 21)
      • 21. Zhou, B., Lin, Z., Duan, G.: ‘Truncated predictor feedback for linear systems with long time-varying input delay’, Automatica, 2012, 48, pp. 23872399.
    22. 22)
      • 22. Yoon, S.Y., Lin, Z.: ‘Truncated predictor feedback control for exponentially unstable linear systems with time-varying input delay’, Syst. Control Lett., 2013, 62, pp. 837844.
    23. 23)
      • 23. Yoon, S.Y., Anantachaisilp, P., Lin, Z.: ‘An LMI approach to the control of exponentially unstable systems with input time delay’. Proc. 52nd IEEE Conf. Decision Control, CDC, Firenze, Italy, 2013, pp. 312317.
    24. 24)
      • 24. Ding, Z., Lin, Z.: ‘Truncated state prediction for control of Lipschitz nonlinear systems with input delay’. Proc. 53rd IEEE Conf. Decision Control, CDC, Los Angeles, CA, USA, 2014, pp. 19661971.
    25. 25)
      • 25. Bresch-Pietri, D., Krstic, M.: ‘Delay-adaptive predictor feedback for systems with unknown long actuator delay’, IEEE Trans. Autom. Control, 2010, 55, pp. 21062112.
    26. 26)
      • 26. Wang, C., Zuo, Z., Lin, Z., , et al: ‘Consensus control of a Class of Lipschitz nonlinear systems with input delay’, IEEE Trans. Circuits Syst. I, Regul. Pap., 2015, 62, pp. 27302738.
    27. 27)
      • 27. Wang, C., Ding, Z.: ‘H Consensus control of multi-agent systems with input delay and directed topology’, IET Control Theory Appl., 2016, 10, pp. 617624.
    28. 28)
      • 28. Zuo, Z., Wang, C., Ding, Z.: ‘Robust consensus control of uncertain multi-agent systems with input delay: a model reduction method, Int. J. Robust Nonlinear Control, 2017, 27, pp. 18741894.
    29. 29)
      • 29. Wang, C., Zuo, Z., Lin, Z., , et al: ‘A truncated prediction approach to consensus control of Lipschitz nonlinear multi-agent systems with input delay’, IEEE Trans. Control Netw. Syst., Published online, doi: 10.1109/TCNS.2016.2545860..
    30. 30)
      • 30. Zuo, Z., Lin, Z., Ding, Z.: ‘ Truncated predictor control of Lipschitz nonlinear systems with time-varying input delay’, IEEE Trans. Autom. Control, 2017, 62, pp. 53245330.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2017.0286
Loading

Related content

content/journals/10.1049/iet-cta.2017.0286
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address