High-Gain Observer Design for Nonlinear Systems with Delayed Output Measurements using Time-Varying Gains

Ania Adil*, Ibrahima N'Doye, Taous Meriem Laleg-Kirati

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This paper proposes a high-gain observer design for nonlinear systems with delayed output measurements using time-varying gains. The proposed observer is endowed with an exponential stability guarantee and relies on the generalization of the Halanay-type inequalities. We establish that the estimated state and the adapted gain are exponentially bounded and prevent the oscillatory response of the estimates. The time-varying gain feature limits the constant high-gain values of the standard high-gain observer design to the minimum gain required to achieve stability. Furthermore, we derive an explicit relation between the maximum bound of the delay and the maximum gain parameter by using a Lyapunov-Krasovskii functional jointly with the time-varying Halanay inequality. Finally, a comparison with the standard high-gain observer is provided through numerical simulations to demonstrate the superiority of the proposed high-gain observer in rejecting the noise and reducing the peaking phenomena.

Original languageEnglish (US)
Title of host publication2022 IEEE 61st Conference on Decision and Control, CDC 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781665467612
StatePublished - 2022
Event61st IEEE Conference on Decision and Control, CDC 2022 - Cancun, Mexico
Duration: Dec 6 2022Dec 9 2022

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference61st IEEE Conference on Decision and Control, CDC 2022

Bibliographical note

Funding Information:
This work has been supported by the King Abdullah University of Science and Technology (KAUST), Base Research Fund (BAS/1/1627-01-01) to Taous-Meriem Laleg-Kirati. Ania Adil thanks the Direction Générale de la Recherche Scientique et du Développement Technologique DGRSDT/MESRS-Algeria for the financial support.

Publisher Copyright:
© 2022 IEEE.


  • disturbance rejection
  • High-gain observer
  • nonlinear observer
  • nonlinear triangular systems
  • peaking attenuation
  • time-varying gain

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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