Robust Stabilization of Nonlinear Globally Lipschitz Delay Systems

  • Tarek Ahmed-Ali
  • Iasson Karafyllis
  • Miroslav Krstic
  • Francoise Lamnabhi-Lagarrigue
Part of the Advances in Delays and Dynamics book series (ADVSDD, volume 4)


This paper studies the application of a recently proposed control scheme to globally Lipschitz nonlinear systems for which the input is delayed and applied with zero order hold, the measurements are sampled and delayed, and only an output is measured (i.e., the state vector is not available). The control scheme consists of an observer for the delayed state vector, an inter-sample predictor for the output signal, an approximate predictor for the future value of the state vector, and the nominal feedback law applied with zero order hold and computed for the predicted value of the future state vector. The resulting closed-loop system is robust with respect to modeling and measurement errors and robust to perturbations of the sampling schedule.


  1. 1.
    Bekiaris-Liberis, N., Krstic, M.: Robustness of nonlinear predictor feedback laws to time-and state-dependent delay perturbations. Automatica 49(6), 1576–1590 (2013)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bekiaris-Liberis, N., Krstic, M.: Nonlinear Control Under Nonconstant Delays. SIAM, Philadelphia (2013)MATHCrossRefGoogle Scholar
  3. 3.
    Karafyllis, I., Krstic, M.: Nonlinear stabilization under sampled and delayed measurements, and with inputs subject to delay and zero-order hold. IEEE Trans. Autom. Control 57(5), 1141–1154 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Krstic, M.: Delay Compensation for Nonlinear, Adaptive, and PDE Systems. Birkhauser, Boston (2009)MATHCrossRefGoogle Scholar
  5. 5.
    Krstic, M.: Input delay compensation for forward complete and strict-feedforward nonlinear systems. IEEE Trans. Autom. Control 55(2), 287–303 (2010)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Karafyllis, I.: Stabilization by means of approximate predictors for systems with delayed input. SIAM J. Control Optim. 49(3), 1100–1123 (2011)MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Karafyllis, I., Krstic, M.: Stabilization of nonlinear delay systems using approximate predictors and high-gain observers. Automatica 49(12), 3623–3631 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Karafyllis, I., Krstic, M.: Numerical schemes for nonlinear predictor feedback. Math. Control Signals Systems 26(4), 519–564 (2014)MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Karafyllis, I., Malisoff, M., de Queiroz, M., Krstic, M., Yang, R.: Predictor-based tracking for neuromuscular electrical stimulation. Int. J. Robust Nonlinear Control doi: 10.1002/rnc.3211
  10. 10.
    Ahmed-Ali, T., Karafyllis, I., Lamnabhi-Lagarrigue, F.: Global exponential sampled-data observers for nonlinear systems with delayed measurements. Syst. Control Lett. 62(7), 539–549 (2013)MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Germani, G., Manes, C., Pepe, P.: A new approach to state observation of nonlinear systems with delayed output. IEEE Trans. Autom. Control 47(1), 96–101 (2002)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Karafyllis, I., Krstic, M., Ahmed-Ali, T., Lamnabhi-Lagarrigue, F.: Global stabilization of nonlinear delay systems with a compact absorbing set. Int. J. Control 87(5), 1010–1027 (2014)MATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Sun, X.-M., Liu, K.-Z., Wen, C., Wang, W.: Predictive control of nonlinear continuous networked control systems with large time-varying transmission delays and transmission protocols. Personal Communication (2014)Google Scholar
  14. 14.
    Karafyllis, I., Jiang, Z.-P.: Stability and Stabilization of Nonlinear Systems. Springer-verlag, London (2011)MATHCrossRefGoogle Scholar
  15. 15.
    Heemels, W., Teel, A., van de Wouw, N., Nesic, D.: Networked control systems with communication constraints: tradeoffs between transmission intervals, delays and performance. IEEE Trans. Autom. Control 55(8), 1781–1796 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Tarek Ahmed-Ali
    • 1
  • Iasson Karafyllis
    • 2
  • Miroslav Krstic
    • 3
  • Francoise Lamnabhi-Lagarrigue
    • 4
  1. 1.Laboratoire GREYC CNRS-ENSICAENCaen CedexFrance
  2. 2.Department of MathematicsNational Technical University of AthensAthensGreece
  3. 3.Department of Mechanical and Aerospace EngineeringUniversity of CaliforniaLa JollaUSA
  4. 4.Centre National de la Recherche ScientifiqueGif-Sur-YvetteFrance

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