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

  • Boubekeur Targui
  • Omar Hernández-GonzálezEmail author
  • Carlos-Manuel Astorga-Zaragoza
  • Gerardo-Vicente Guerrero-Ramírez
  • María-Eusebia Guerrero-Sánchez
Regular Papers Control Theory and Applications
  • 34 Downloads

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.

Keywords

Lyapunov-Krasovskii and linear matrix inequality time-varying delay 

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References

  1. [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. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [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. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [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.CrossRefGoogle Scholar
  8. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [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.CrossRefzbMATHGoogle Scholar
  10. [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.MathSciNetGoogle Scholar
  11. [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. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [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.CrossRefGoogle Scholar
  15. [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. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [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. [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.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Boubekeur Targui
    • 1
  • Omar Hernández-González
    • 2
    Email author
  • Carlos-Manuel Astorga-Zaragoza
    • 3
  • Gerardo-Vicente Guerrero-Ramírez
    • 3
  • María-Eusebia Guerrero-Sánchez
    • 2
  1. 1.Laboratoire d’Automatique de CaenUniversité de Caen NormandieCaen CedexFrance
  2. 2.Tecnológico Nacional de México / Instituto Tecnológico Superior de CoatzacoalcosCoatzacoalcos, Ver.Mexico
  3. 3.Tecnológico Nacional de México / Centro Nacional de Investigación y Desarrollo Tecnológico, CENIDET, Interior Internado Palmira s/nCol. PalmiraCuernavaca, Mor.Mexico

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