An LMI-based discrete time nonlinear observer for Light-Emitting Diode optical communication

Ibrahima N'Doye, Ding Zhang, Ania Adil, Ali Zemouche, Rajesh Rajamani, Taous Meriem Laleg-Kirati

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Light-Emitting Diode (LED) optical wireless communication is a potentially low-cost, sustainable approach for enabling high-speed free-space and underwater transmissions within a limited communication range. Establishing a tightly controlled line of sight (LOS) between transmitter and receiver is a significant challenge because the angle of the alignment is not directly measured and has to be estimated. To address this problem, we propose a novel switched-gain discrete-time nonlinear observer for an LED-based optical communication model in which the nonlinear output functions are composed of nonlinear vector functions of multi-scalar combinations of the states. Lyapunov function-based analysis that ensures global stability is used to design the proposed observer in each piecewise monotonic region of the LED output functions. Furthermore, we prove via a quadratic Lyapunov-based approach that a constant stabilizing observer gain design approach has no feasible solution when the entire LED optical communication range is considered. Therefore, a suitable switched-gain nonlinear observer is derived for non-monotonic output measurement equations. Simulation results are shown together with extensive comparisons with the Extended Kalman Filter (EKF) to illustrate the performance of the proposed switched-gain observer design.

Original languageEnglish (US)
Article number110309
StatePublished - Jul 2022

Bibliographical note

Funding Information:
This work has been supported by the King Abdullah University of Science and Technology (KAUST), Saudi Arabia through Base Research Fund ( BAS/1/1627-01-01 ). 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 Angelo Alessandri under the direction of Editor Thomas Parisini.

Funding Information:
Rajesh Rajamani (Fellow, IEEE) received the B.Tech. degree from the Indian Institute of Technology Madras, Chennai, India, in 1989, and the M.S. and Ph.D. degrees from the University of California, Berkeley, CA, USA, in 1991 and 1993, respectively. He is currently the Benjamin Y.H. Liu-TSI Endowed Professor of Mechanical Engineering and Associate Director (Research) of the Minnesota Robotics Institute, University of Minnesota, Minneapolis, MN, USA. He has coauthored more than 170 journal papers and is a co-inventor on 17 patent applications. He is the author of the popular book Vehicle Dynamics and Controlpublished by Springer Verlag. His active research interests include estimation, sensing and control for smart mechanical systems. He was the Chair of the IEEE CSS Technical Committee on Automotive Control and is currently a Senior Editor of the IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS. Dr. Rajamani is a Fellow of IEEE and ASME and was the recipient of the CAREER Award from the National Science Foundation, the Ralph Teetor Award from SAE, the O. Hugo Schuck Award from the American Automatic Control Council, and a number of best paper awards from conferences and journals. Several inventions from his laboratory have been commercialized through start-up ventures co-founded by industry executives. One of these companies, Innotronics, was recently recognized among the 35 Best University Start-Ups of 2016 in a competition conducted by the US National Council of Entrepreneurial Tech Transfer.

Publisher Copyright:
© 2022 The Author(s)


  • Light-emitting diode (LED) optical communication
  • Linear matrix inequality (LMI) approach
  • Monotonic systems
  • Nonlinear observer design
  • Optical wireless communication
  • Switched systems


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