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Generalized Multiple Delay-dependent H∞, Functional Observer Design for Nonlinear System

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  • Control Theory and Applications
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Abstract

Functional observers are the major alternative to many practical estimation problems where full-order observers cannot be used. This paper introduces a generalized approach to design H∞ functional observers for a class of Lipschitz nonlinear systems with multiple time delays. Moreover, the considered system extends from previously published work in that it presents nonlinearity, multiple delay and external disturbance. Their main findings come from the development of a generalized augmented Lyapunov function that uses both the extended reciprocal convex combination and the Wirtinger inequality. The stability of the observer is therefore guaranteed by an LMI optimization problem. Finally, the steps of the design procedure were condensed and proffered for the two numerical examples to test the recommended design approach.

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Data Availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, BP 72 Imouzzer Road, Fez, Morocco

    Ghali Naami & Mohamed Ouahi

  2. Institute of Durable Processes and Doctoral School, School of Industrial Engineering, University of Valladolid, Valladolid, 47005, Spain

    Teresa Alvarez

  3. Modeling Information and Systems (MIS) Laboratory, University of Picardie Jules Verne, 33 Rue St Leu, Amiens, France

    Abdelhamid Rabhi

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  1. Ghali Naami
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Correspondence to Teresa Alvarez.

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The authors declared that they have no conflicts of interest to this work.

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Ghali Naami recieved his master’s degree in signals systems and informatics from the Faculty of Sciences at University Of Sidi Mohamed Ben Abdelah, Fez, Morocco, in 2017 and a Ph.D. degree in electrical engineering in 2022 from the National School of Applied Sciences at the same University. His current research interests include functional and dynamic observers, time-delay systems, traffic flow modeling and control, and linear and nonlinear systems.

Mohamed Ouahi received his sciences degree in automatic systems and image in 2008 and a Ph.D. degree in computer engineering and automatic in 2011 from National School of Engineers of Limoge France. He has been a professor at National School of Applied Sciences, Fes, Morocco, since 2013. His current research interests include nonlinear control theory, state observer, automotive supervision, and singular systems.

Teresa Alvarez is an associate professor at the School of Engineering of the University of Valladolid, Spain (since 1995). She graduated from the University of Oviedo in computer science in 1989, from the University of Valladolid in computer engineering in 1992, and from the University of Bradford, UK, in control engineering (M.Sc.). She obtained her Ph.D. degree in automatic control from the University of Valladolid in 1994. Her current interest lies in computer-controlled systems (focusing on congestion control in computer networks) and linear and nonlinear control.

Abdelhamid Rabhi is a professor at the Faculty of Sciences and Picardie Jules Verne University of Amiens in France. He completed his master’s degree in robotics and control systems from the University of Versailles, and a Ph.D. degree in observation and control for nonlinear and complex systems in December 2005. His research deals with robust control, diagnosis and observation for complex systems with focus on areas such as vehicles, autonomous robots applications, and renewable energy systems.

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Naami, G., Ouahi, M., Alvarez, T. et al. Generalized Multiple Delay-dependent H∞, Functional Observer Design for Nonlinear System. Int. J. Control Autom. Syst. 21, 3584–3594 (2023). https://doi.org/10.1007/s12555-023-0087-2

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  • DOI: https://doi.org/10.1007/s12555-023-0087-2

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