Skip to main content
SpringerLink
Log in

A New Observer Design for Systems in Presence of Time-varying Delayed Output Measurements

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

Abstract

This paper presents a state observer for linear systems and Lipschitz nonlinear systems with delayed output measurements, which are affected by a known and bounded time-varying delay. The structure of the proposed observer is based on a proportional-integral term, which allows to compensate the time-varying delay. The observer gain depends on the maximum bounded delay. This gain is computed by a Linear Matrix Inequality (LMI) approach. The observer exhibits good performance for state estimation of the system despite the presence of significantly long delay. A Lyapunov-Krasovskii functional is used to prove the asymptotical convergence to zero of the observation error. This observer is applied to the case of systems with time-varying delay whose dynamic is described by a piecewise differentiable function. Examples and numerical simulations are provided in order to support the validity of the main 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.

Similar content being viewed by others

References

  1. V. V. Assche, T. Ahmed–Ali, C.A.B. Hann, and F. Lamnabhi–Lagarrigue, “High gain observer design for nonlinear systems with time varying delayed measurements,” Proc. of the 18thWorld Congress, pp. 692–696, Aug. 2011.

    Google Scholar 

  2. N. Bekiaris–Liberis and M. Krstic, “Compensation of State–Dependent Input Delay for Nonlinear Systems,” IEEE Trans. on Automatic Control, vol. 58, no. 2, pp. 275–289, Feb. 2013.

    Article  MathSciNet  MATH  Google Scholar 

  3. G. Besancon, D. Georges, and Z. Benayache, “Asymptotic state prediction for continuous–time systems with delayed input and application to control,” Proc. of European Control Conference, pp. 1786.1791, Kos, Greece, July 2007.

    Google Scholar 

  4. F. Cacace, A. Germani and C. Manes, “An observer for a class of nonlinear systems with time–varying observation delay,” Systems & Control Letters, vol. 59, no. 5, pp. 305–312, May 2010.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Darouach, “Linear functional observers for systems with delays in state variables,” IEEE Trans. on Automatic Control, vol. 46, no. 3, pp. 491–496, Mar. 2001.

    Article  MathSciNet  MATH  Google Scholar 

  6. A. Germani, C. Manes, and P. Pepe, “A new approach to state observation of nonlinear systems with delayed output,” IEEE Trans. on Automatic Control, vol. 47, no. 1, pp. 96–101, Aug. 2002.

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Houimli, N. Bedioui, and M. Besbes, “An improved polytopic adaptive LPV observer design under actuator fault,” International Journal of Control, Automation and Systems, vol. 16, no. 1, pp. 168–180, Mar. 2018.

    Article  Google Scholar 

  8. N. Kazantzis and R. A. Wright, “Nonlinear observer design in the presence of delayed output measurements,” Systems & Control Letters, vol. 54, no. 9, pp. 877–886, Sep. 2005.

    Article  MathSciNet  MATH  Google Scholar 

  9. 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, April 2016.

    Article  MATH  Google Scholar 

  10. J. Lei and H.–K. Khalil, “High–gain–predictor–based output feedback control for time–delay nonlinear systems,” Automatica, vol. 71, no. 1, pp. 324333, Sep. 2016.

    MathSciNet  Google Scholar 

  11. J. Lu, C. Feng, S. Xu, and Y. Chu, “Observer design for a class of uncertain state–delayed nonlinear systems,” International Journal of Control, Automation, and Systems, vol. 4, no. 4, pp. 448–455, Aug. 2006.

    Google Scholar 

  12. S. Mobayen, “Robust tracking controller for multivariable delayed systems with input saturation via composite nonlinear feedback,” Nonlinear Dynamics, vol. 76, no. 1, pp 827–838, Dec. 2013.

    Article  MathSciNet  MATH  Google Scholar 

  13. S. Mondie and W. Michiels, “Finite spectrum assignment of unstable time–delay systems with a safe implementation,” IEEE Trans. on Automatic Control, vol. 48, no. 12, pp. 2207–2212, Dec. 2003.

    Article  MathSciNet  MATH  Google Scholar 

  14. S. Santra, H. R. Karimi, R. Sakthivel, and S. Marshal Anthoni, “Dissipative based adaptive reliable sampleddata control of time–varying delay Systems,” International Journal of Control, Automation, and Systems, vol. 14, no. 1, pp. 39–50, Feb. 2016.

    Article  Google Scholar 

  15. K. Subbarao and P. C. Muralidhar, “A state observer for LTI systems with delayed outputs: time–varying delay,” Proc. of American Control Conference, pp. 3029.3033, Seattle, USA, June 2008.

    Google Scholar 

  16. Y. Wang, D. Zhao, Y. Li, and S. X. Ding, “Unbiased minimum variance fault and state estimation for linear discrete time–varying two–dimensional systems,” IEEE Trans. on Automatic Control, vol. 62, no. 10, pp. 5463–5469, April 2017.

    Article  MathSciNet  MATH  Google Scholar 

  17. D. Zhao, D. Shen, and Y. Wang, “Fault diagnosis and compensation for two–dimensional discrete time systems with sensor faults and time–varying delays,” International Journal of Robust and Nonlinear Control, vol. 27, no. 16, pp. 3296–3320, Dec. 2016.

    Article  MathSciNet  MATH  Google Scholar 

  18. Y. Zhao, J. Tao, and N.–Z. Shi, “A note on observer design for one–sided Lipschitz nonlinear systems,” Systems & Control Letters, vol. 59, no. 1, pp. 66–71, Jan. 2010.

    Article  MathSciNet  MATH  Google Scholar 

  19. G. Zheng and F.–J. Bejaranoc, “Observer design for linear singular time–delay systems,” Automatica, vol 80, no. 1, pp. 1–9, June 2017.

    Google Scholar 

  20. M. Zhong, D. Zhou, and S. X. Ding, “On designing H¥ fault detection filter for linear discrete time–varying systems,” IEEE Trans. on Automatic Control, vol. 55, no. 7, pp. 1689–1695, July 2010.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire d’Automatique de Caen, Université de Caen Normandie, 6 Boulevard du Maréchal Juin, 14050, Caen Cedex, France

    Boubekeur Targui

  2. Tecnológico Nacional de México / Instituto Tecnológico Superior de Coatzacoalcos, Carretera Ant. Mina-Coatza Km. 16.5, Col. Reserva Territorial, CP 96536, Coatzacoalcos, Ver., Mexico

    Omar Hernández-González & María-Eusebia Guerrero-Sánchez

  3. Tecnológico Nacional de México / Centro Nacional de Investigación y Desarrollo Tecnológico, CENIDET, Interior Internado Palmira s/n, Col. Palmira, CP 62490, Cuernavaca, Mor., Mexico

    Carlos-Manuel Astorga-Zaragoza & Gerardo-Vicente Guerrero-Ramírez

Authors
  1. Boubekeur Targui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Omar Hernández-González
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Carlos-Manuel Astorga-Zaragoza
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gerardo-Vicente Guerrero-Ramírez
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. María-Eusebia Guerrero-Sánchez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Omar Hernández-González.

Additional information

Recommended by Associate Editor Nam H. Jo under the direction of Editor PooGyeon Park.

Boubekeur Targui received the Ph.D. degrees in control engineering from the University of Claude Bernard Lyon I, Lyon, France, in 2000. Since 2002, he has held a position of Associate Professor in University de Caen, France. His current research interests are in nonlinear observers and automatic control.

Omar Hernandez-Gonzalez received his M.Sc. degree in electronic engineering from CENIDET, México, in 2008, and the Ph.D. degree in automatic from the University of Caen Normandie, France, in 2017. Since 2008, he has held a position of Professor in the Technological Institute of México / Coatzacoalcos (ITESCO). His research interests include the nonlinear observers.

Carlos-Manuel Astorga-Zaragoza received the Ph.D. degree in process engineering from the University of Claude Bernard Lyon 1, France, in 2001. Since 1993, he has held teaching and research positions at the CENIDET, where he mainly works on observers and fault detection systems for energy conversion processes.

Gerardo-Vicente Guerrero-Ramírez received the Ph.D. degree in Engineering from the Universidad Nacional Autónoma de México (UNAM), México, in 2001. He is currently a professor of department of electronic engineering at the Centro Nacional de Investigación y Desarrollo Tecnológico (CENIDET).

María-Eusebia Guerrero-Sánchez received the Ph.D. degree in electronic engineering from the Centro Nacional de Investigación y Desarrollo Tecnológico (CENIDET), México, in 2017. She is currently a Professor of the Technological Institute of México / Coatzacoalcos (ITESCO). Her research interests are focused on passivity-based control, nonlinear control, and UAV.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Targui, B., Hernández-González, O., Astorga-Zaragoza, CM. et al. A New Observer Design for Systems in Presence of Time-varying Delayed Output Measurements. Int. J. Control Autom. Syst. 17, 117–125 (2019). https://doi.org/10.1007/s12555-017-0224-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-017-0224-x

Keywords

Search

Navigation