Regular Papers

International Journal of Control, Automation, and Systems 2023; 21(11): 3584-3594

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

© The International Journal of Control, Automation, and Systems

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

Ghali Naami, Mohamed Ouahi, Teresa Alvarez*, and Abdelhamid Rabhi

University of Valladolid

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.

Keywords Disturbances, functional observers, linear matrix inequalities (LMIs), Lyapunov functions, nonlinear systems, time delays.

Article

Regular Papers

International Journal of Control, Automation, and Systems 2023; 21(11): 3584-3594

Published online November 1, 2023 https://doi.org/10.1007/s12555-023-0087-2

Copyright © The International Journal of Control, Automation, and Systems.

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

Ghali Naami, Mohamed Ouahi, Teresa Alvarez*, and Abdelhamid Rabhi

University of Valladolid

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.

Keywords: Disturbances, functional observers, linear matrix inequalities (LMIs), Lyapunov functions, nonlinear systems, time delays.

IJCAS
July 2024

Vol. 22, No. 7, pp. 2055~2340

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