New H_∞ dynamic observer design for time-delay systems subject to disturbances

Abstract

This paper presents a new approach to design an H${}_{\mathrm{\infty }}$ dynamic observer (DO) for multi-delayed linear systems subject to ${\mathcal{L}}_2$-norm disturbances. This observer generalises the existing results on the proportional observer (PO), the proportional integral observer (PIO), and the DO. The proposed design approach is derived from the solution of LMIs based on the parametrization results of algebraic constraints. These algebraic constraints can be easily obtained from the unbiasedness conditions of the estimation error. The obtained results are illustrated by a numerical example to show the performances of the proposed observer.

Keywords:

• H${}_{\mathrm{\infty }}$ dynamic observer
• multi-delayed systems
• disturbances
• unbiasedness conditions
• estimation error

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

El Fezazi Nabil

El Fezazi Nabil received his Master's degree in Engineering of Automated Industrial Systems and his Doctorate (Ph.D) in Electrical Engineering from the Sidi Mohammed Ben Abdellah University, Faculty of Sciences, Morocco in 2013 and 2018, respectively. His main research interests are Robust and H_∞ Control, Observer-Based Control, Sampled-Data Control, Vehicle Dynamics, TCP/IP Networks, Quadruple Tank Process, and Wind Tunnel.

Frih Abderrahim

Frih Abderrahim received his Master's degree in Engineering of Automated Industrial Systems in 2013 from the Sidi Mohammed Ben Abdellah University, Morocco, and his Ph.D in Electrical Engineering in 2018 from the same university. His main research interests are Automation, Bond Graph, Modelling, Observer, and Intelligent Control.

Lamrabet Ouarda

Lamrabet Ouarda received her Master's degree in Signals Systems and Computer Science from the Sidi Mohammed Ben Abdellah University, Faculty of Sciences, Morocco in 2015. She is currently a Ph.D student in the same faculty. Her main research interests are Robust and H_∞ Control, Sampled-Data Control, and Systems with Saturating Actuators.