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


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.


Lyapunov-Krasovskii and linear matrix inequality time-varying delay 


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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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