In this paper, we propose a high-gain observer design for nonlinear systems with time-varying delayed output measurements. Based on a recent high-gain like observer design method, called HG/LMI observer, a larger bound of the time-delay is allowed compared to that obtained by using the standard high-gain methodology. Such a HG/LMI observer adopts a lower value of the tuning parameter, which results in the reduction of the value of the observer gain, and an increase in the maximum bound of the delay required to ensure exponential convergence. Indeed, an explicit relation between the maximum bound of the delay and the observer tuning parameter is derived by using a Lyapunov–Krasovskii functional jointly with the Halanay inequality. Such a relation shows clearly the superiority of HG/LMI observer design methodology. An application to nonlinear systems with sampled measurements is provided. Furthermore, the proposed methodology is extended to systems with nonlinear outputs. This extension provides more general synthesis conditions and encompasses the linear case as a particular situation. Finally, two numerical examples are proposed to illustrate the performance of the proposed observer design procedure, and comparison to standard approaches is also provided.
Bibliographical noteFunding Information:
This work was partially funded by the ANR, France agency via the project ArtISMo ANR-20-CE48-0015 coordinated by A. Zemouche. The material in this paper was partially presented at the 21st IFAC World Congress (IFAC 2020), July 12-17, 2020, Berlin, Germany. This paper was recommended for publication in revised form by Associate Editor Juan C. Aguero under the direction of Editor Torsten S?derstr?m.This work has been partially supported by the King Abdullah University of Science and Technology (KAUST), Saudi Arabia, Base Research Fund (BAS/1/1627-01-01) to Taous-Meriem Laleg-Kirati. A. Zemouche thanks the CRAN-UMR CNRS 7039, and the IUT Henri Poincar? de Longwy for the partial support of this work.
This work has been partially supported by the King Abdullah University of Science and Technology (KAUST), Saudi Arabia , Base Research Fund ( BAS/1/1627-01-01 ) to Taous-Meriem Laleg-Kirati. A. Zemouche thanks the CRAN-UMR CNRS 7039, and the IUT Henri Poincaré de Longwy for the partial support of this work.
© 2022 Elsevier Ltd
- Delayed output measurements
- High-gain observer
- Linear matrix inequalities (LMIs)
- Lyapunov–Krasovskii functionals
- Nonlinear systems
ASJC Scopus subject areas
- Control and Systems Engineering
- Electrical and Electronic Engineering